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posts updates from arXiv rss feeds for methodology papers in Statistics and Econometrics. Also maintains an arxiv and posts random papers from it. maintainer: @apoorvalal.com source code: https://github.com/apoorvalal/bsky_paperbot

$Effect modification occurs when the impact of the treatment on an outcome varies based on the levels of other covariates known as effect modifiers. Modeling of these effect differences is important for etiological goals and for purposes of optimizing treatment. Structural nested mean models (SNMMs) are useful causal models for estimating the potentially heterogeneous effect of a time-varying exposure on the mean of an outcome in the presence of time-varying confounding. In longitudinal health studies, information on many demographic, behavioural, biological, and clinical covariates may be available, among which some might cause heterogeneous treatment effects. A data-driven approach for selecting the effect modifiers of an exposure may be necessary if these effect modifiers are \textit{a priori} unknown and need to be identified. Although variable selection techniques are available in the context of estimating conditional average treatment effects using marginal structural models, or in the context of estimating optimal dynamic treatment regimens, all of these methods consider an outcome measured at a single point in time. In the context of an SNMM for repeated outcomes, we propose a doubly robust penalized G-estimator for the causal effect of a time-varying exposure with a simultaneous selection of effect modifiers and prove the oracle property of our estimator. We conduct a simulation study to evaluate the performance of the proposed estimator in finite samples and for verification of its double-robustness property. Our work is motivated by a study of hemodiafiltration for treating patients with end-stage renal disease at the Centre Hospitalier de l'Universit\'e de Montr\'eal.$

Estimating causal effects under interference is a common problem in social science and economics. However, it is challenging due to the complex dependency structure induced by network connections. In this paper, we propose GAUGER, a Generalized regression Adjustment framework via Graph-weighted Exposure-level Residualization for design-based causal inference under general interference. We first reveal a surprising mismatch between accuracy and efficiency in this setting: model adjustments that minimize prediction error (e.g., MSE) do not necessarily lead to the most variance reduction of the treatment effect estimator. To address this mismatch, we propose a two-step approach: (1) leveraging a strong prediction model to learn outcome patterns from the network and covariates, and (2) applying a novel calibration scheme called Graph-weighted Exposure-level Residualization (GER) that directly targets variance reduction. The resulting estimator is consistent for target causal parameters, enjoys provable variance reduction, and is asymptotically normal with a conservative variance estimator for valid statistical inference. As a practical implementation of the pipeline, we present a scheme that leverages Graph Neural Networks (GNNs) to construct the prediction model and use GER to steer the model adjustment for better variance reduction. Numerical studies show substantial efficiency gains over existing methods.

$Consider the partial linear model $Y = \mu_0(X) + \beta_0 \cdot T + \varepsilon$ and $T = \pi_0(X) + u$ in the structure-agnostic setting, where we are blind to the structure $\mu_0$ and $\pi_0$ and estimate the nuisances by a black-box hypothesis class. The learnability of the class is characterized by the estimation error $\delta_s$ in the absence of model misspecification and its $L_2$ mis-specification error $\delta_{a, \mu}$ and $\delta_{a, \pi}$ for $\mu_0$ and $\pi_0$, respectively. We propose a novel estimator of the target linear coefficient $\theta_0 = \beta_0$ with error rate \[ \frac{1}{\sqrt{n}} + \delta_{a, \mu} \cdot \delta_{a, \pi} + [\delta_s]^2. \] A matching lower bound is also established, implying that this rate is unimprovable. Compared with the product rate yielded by double machine learning (DML), our estimator removes the suboptimal term $\max(\delta_{a, \mu}, \delta_{a, \pi})\cdot \delta_s$ at no extra cost or assumption. Building on the underlying insights, which are neither tailored to the one-learner setting nor the partial linear model, we propose Transductive Adversarial Moment-calibrated Editing (TAME), which locally edits debiasing weights induced by black-box regression estimates on the inference sample through adversarial conditional moment calibration. TAME can be combined with any initial black-box estimates and can strictly improve on DML guarantees when the nuisance difficulties are imbalanced. We discuss how to fully exploit the advantages introduced by TAME, including the gains from using two learners, the resulting under-smoothing principle for model selection, and extensions to other linear functional estimation problems.$

The rise of human-AI collaborative writing has created a growing need for fine-grained detection methods that support localizing likely LLM-generated content in mixed-authorship documents. Existing methods for detecting LLM-generated text mainly focus on document-level classification and cannot identify which parts of the text are generated by LLMs. This paper introduces a new method to address this urgent need. Our method operates at the token level, the natural unit of modern language models, and builds on existing token-level detection scores. The key idea is to smooth adjacent token scores to reduce their variability, while using an adaptive Lepski-type rule to select the bandwidth according to the local authorship structure. Our method is simple to implement and does not require token-level labeled data for training. Theoretically, we characterize this trade-off and show that the proposed method achieves favorable mean square error performance in estimating the underlying signal. Empirically, we demonstrate strong performance of our method against a wide range of baselines in both synthetic datasets and a realistic dataset. We deploy a publicly accessible website that implements the methods as well.

Mobile-health interventions increasingly use online learning and decision making algorithms to personalize when to nudge users toward healthier behavior, but a poorly designed algorithm can burden and disengage participants. New algorithm design decisions should therefore be vetted against realistic simulated users before each real-life deployment. We propose a method to develop ``JITAI-Twins'': digital twins of a target subpopulation for comparing candidate online algorithms before a just-in-time adaptive intervention (JITAI) deployment. The method builds on a conditional time-series diffusion model that is temporally consistent (future actions do not affect the generated past), and it supports repeated updating from three sources of information, in three steps: pre-training on a large observational dataset, fine-tuning on small prior intervention deployments in related populations, and inference-time calibration to the next target population from domain-scientist expertise. We validate the twin at each pre-deployment stage of the long-running HeartSteps series (v2 through v4) of physical-activity suggestion intervention deployments, treating each successive deployment as an upcoming study. The proposed method reproduces the target subpopulation's temporal and between-participant structure better than simpler simulators. These results suggest that our twin can be used to simulate a target deployment before it runs, the prerequisite for testing and informing online algorithm design decisions.

Existing methods for risk-limiting audits typically focus on certifying individual contests. In parliamentary elections, however, the politically relevant outcome is often whether a party has won enough seats to form government, not whether every reported seat outcome is correct. Extending on the work of Mohanty et al. (2019), we formulate the certification of a parliamentary majority as a partial conjunction testing problem: it is enough to verify that the reported winning party truly won at least a majority of its reported seats. Building on the SHANGRLA auditing framework, we construct a sequential audit statistic for the majority outcome by combining seat-level statistics. We then propose adaptive sampling strategies that allocate auditing effort across seats, including variants that learn to avoid spending excessive effort on seats that appear unlikely to have been truly won. Using simulations based on synthetic and real data, from the 2014 Indian Lok Sabha election, we show that auditing the parliamentary majority can substantially reduce the number of ballots inspected (by almost a thousand-fold) compared to certifying every reported winning seat.

Civic AI systems increasingly support democratic participation, yet interactions with them may reveal sensitive political views, creating tension between improving AI models and residents' expectations of privacy and consent. This study examines the conditions of transparency and user control under which Swiss residents are willing to donate their anonymized chatbot conversations to train an open-source AI model. A 2x2 between-subjects factorial design evaluated how a Data Nutrition Label and a granular consent dashboard influence donation decisions. The experiment was delivered via a multilingual online survey featuring a custom chatbot powered by the Apertus-70B model. Analysis of the 205 participants revealed that neither transparency nor control significantly affected donation behavior. Rates were uniformly high (91.7% overall), producing a ceiling effect, and Bayesian checks confirmed the absence of treatment effects. The dashboard raised perceived control but not donation, and high-control participants actively restricted their data-use settings. A qualitative analysis of 120 open-ended responses indicates that residents framed donation as a contribution to the public good, motivated by democratic participation, an open-source model, and research, while many regarded their anonymized queries as non-personal and therefore low in risk. Interpreted through the privacy calculus, a high perceived benefit coincided with a low perceived risk under high institutional trust, so both sides of the trade-off aligned and interface design had little leverage. Offering control served less to raise donation than to let residents define the terms of their contribution.

We introduce a self-exciting point process with power-law intensity dynamics that admits a finite-dimensional Markovian state representation. The model is constructed to preserve the local jump and slope update structure of power-law Hawkes processes, while replacing global history dependence with a nonlinear Markov chain governing the intensity dynamics. Within a general state-space framework, we establish irreducibility, aperiodicity, and the T-chain property under mild regularity conditions on the inter-arrival time distribution. Under an explicit stability condition, we further prove that the latent state process is positive Harris recurrent, ensuring the existence of a unique invariant distribution. Simulation results based on the local Whittle estimator show that the proposed Markovian intensity model exhibits long-memory behavior near the boundary of the stability region.

$Many instances of sequential sampling, including audit and inspection scheduling, representative sampling, and treatment assignment, require selections to be distributed evenly without becoming easy to anticipate or exploit. We study a family of sequential sampling rules that adaptively bias sampling probabilities in order to achieve faster convergence of the empirical distribution to a desired target law, while keeping the resulting samples as unpredictable as possible. The resulting self-balancing sampler is simple to implement, arises naturally among a class of Markovian samplers sharing a certain invariance property, and admits a stochastic mirror-descent interpretation. Our main results show that (i) this self-balancing sampler converges at the fastest possible $O(n^{-1})$ rate with explicit dependence on biasing parameters, beating the standard $O(n^{-1/2})$ rate of IID sampling, (ii) it is the unique solution to a natural entropy-regularized optimization problem which balances the convergence rate of the empirical law and the unpredictability of the samples, and (iii) in the weak-biasing regime, the properly centered counts process converges to an Ornstein-Uhlenbeck process in the diffusive limit. Together, these results support a practical framework for reducing repeated selections and long gaps in coverage without making future selections overly predictable.$

Scalar metrics are often used to evaluate clusterings against known classes, but they can obscure a fundamental trade-off: clusterings should be informative about class labels while avoiding unnecessary fragmentation. Here we describe normalized scores of cluster homogeneity and parsimony that quantify this trade-off. These scores build on the information bottleneck principle, modified to not reward lossy compression. We show by example and mathematical proof that our definitions of these scores have the intuitive property of varying monotonically under cluster refinement in contrast to related proposals. Extending the information-theoretic framework beyond Shannon entropies, we furthermore derive set-matching and pair-based counterparts of the homogeneity and parsimony scores. These unify commonly used evaluation criteria and show that, in the pair-based setting, the homogeneity-parsimony trade-off recovers the receiver operating characteristic of binary classifiers. We demonstrate the framework's utility for feature selection and algorithm comparison, illustrating how considering scores jointly can clarify clustering operating points and identify Pareto-optimal solutions.

We propose CEDAR (Causal Edge Discovery for Autoregressive Processes), a constraint-based method for lagged causal edge discovery in sparse autoregressive time series. CEDAR screens candidate cross-variable lags using AR(1)-residualized, U-centered distance correlation, then applies two targeted conditional-independence tests per significant cross-variable lag candidate and accepts at most one lag per ordered pair. A stable MCI pruning step removes indirect edges, and optional deterministic C-nodes adjust for specified trend-like nonstationarity. In sparse regimes where few lags survive screening, CEDAR requires $O(d^2)$ CI tests after screening while retaining edge-level interpretability. CEDAR is most effective when data are scarce and variables exhibit lag-1 self-dynamics; methods with richer conditioning sets become preferable as $T$ grows or when higher-order autoregressive or simultaneous multi-lag effects are common.

The instrumental variable (IV) method is widely used to infer causal effects in observational studies with unmeasured confounding, but invalid instruments can compromise both population identification and finite-sample inference. This paper studies linear IV models with multiple endogenous treatments and possibly invalid instruments. Identification is more delicate than in the single-treatment setting because a single instrument no longer identifies a scalar candidate effect; instead, each relevant instrument defines a hyperplane in the multidimensional effect space. For identification of multiple treatment effects, we introduce generalized plurality and majority rules which require a sufficiently large number of IVs to be valid. For inference, data-dependent instrument selection may fail to separate certain invalid IVs from valid ones, leading to undercoverage of confidence intervals when these invalid instruments are mistakenly selected as valid. We propose a sampling confidence interval for each treatment effect, which is robust to IV selection errors. We establish asymptotic coverage and parametric-rate length of our sampling confidence interval under regularity conditions and illustrate this method in a Mendelian randomization application.

Applied econometricians typically model each individual as having fixed outcomes under treatment and control and, in instrumental-variables (IV) settings, fixed treatment decisions under each value of the instrument. This paper asks what changes when outcomes and treatment allocations or choices are stochastic at the individual level. In the model, each individual has a stable (but possibly stochastic) response type consisting of two objects: a treatment choice probability under each state and a potential outcome distribution under each treatment-state pair. These stochastic potential outcomes change the interpretation of some familiar estimators. For instance, in the deterministic IV model, the estimand identifies treatment effect only for compliers - those whose treatment status switches with the instrument. Under stochastic treatment allocation or choice there is no such subgroup: the estimand averages effects over all individuals, weighting each by how much the instrument, policy, or assignment rule moves their probability of treatment. The paper then gives an information-based foundation for stochastic choice, in which individuals act on expected gains given their information.

This paper develops a profiled sieve minimum-distance estimator for a semi-nonparametric differentiated-products demand model with micro-level choice data. Building on Berry and Haile (2024), the estimator uses within-market variation in consumer covariates to recover a flexible consumer-heterogeneity function and market-specific composite intercepts. Excluded price instruments then separate these intercepts into a flexible price-side function and structural demand shocks. The main statistical challenge is that the number of profiled market intercepts grows with the number of markets. I show that, when both the number of markets and the minimum within-market sample size grow, this profiling step is asymptotically negligible and the common structural functions are uniformly consistently estimated. Monte Carlo evidence supports the consistency result and illustrates the value of flexible price-side estimation for counterfactual demand analysis.

Difference-in-differences (DID) are sometimes estimated with many pre-treatment periods. In such settings, the observed pre-treatment outcome evolutions provide direct information about the magnitude of shocks that could also occur after treatment. This paper proposes a simple inference procedure that uses those pre-trends as the reference distribution for the post-treatment DID. The procedure is closely related to existing conformal inference procedures, but its DID-specific predictor leads to a distinct identifying restriction. Existing procedures assume parallel trends, while this paper's procedure does not require parallel trends.

Structural equation models (SEM) are widely used to describe dependency structures between latent variables, making model selection a key issue in many applications. Existing information criteria are generally based on the integrated observed-data likelihood and therefore do not explicitly account for the latent structure of the model. In this paper, we propose two new information criteria derived from the integrated complete-data likelihood. The first adapts the Integrated Completed Likelihood criterion to Gaussian SEM, while the second proposes an alternative approach to approximating the integrated observed-data log-likelihood by incorporating latent structural information and using an importance sampling strategy. Their performance is assessed through an extensive simulation study covering null, direct, indirect and complete latent structures under different sample sizes and signal strengths. The results show that the proposed importance sampling strategy provides robust and competitive model selection across a wide range of scenarios, whereas the proposed ICL criterion is particularly effective for recovering latent dependency structures when the latent variables are accurately estimated. These findings demonstrate the potential benefits of explicitly exploiting the latent structure when developing information criteria for structural equation models.

The Strang splitting estimator is a powerful estimator for parametric inference in multivariate stochastic differential equation models with nonlinear drift and additive noise. While the choice of splitting does not affect the asymptotic distribution of the estimator, it makes a huge impact in finite-sample settings and it has not yet been shown how the splitting can be chosen optimally. We derive error measures for the transition densities of the Strang splitting scheme, in particular calculating the bias up to the order of $h^3$, where $h$ is the length of the time step. We study the connection between these error measures and the performance of the Strang splitting estimator in the double-well potential model and the stochastic FitzHugh-Nagumo model, respectively. Our simulation studies suggest that linearization around fixed points yields accurate parameter estimates for potential models, while other splittings perform better for slow-fast excitable models.

$We introduce a method for detecting multiple change-points in the mean of a high-dimensional data sequence. Unlike existing top-down (i.e. divisive) algorithms, we adopt a bottom-up (i.e. agglomerative) approach, whereby we iteratively merge neighboring segments of data starting from the finest level. This is particularly useful for signals with frequent change-points, since local evidence is assessed before segments are combined into coarser summaries. We compute $L_2$- and $L_\infty$-aggregated test statistics of neighboring segments and combine the information from their respective ranks, which makes the method adaptive in handling different degrees of change-point sparsity. We show the consistency of the estimated number and locations of change-points under both iid Gaussian and possibly dependent and/or non-Gaussian noise. The practicality of our approach is demonstrated through simulations and a real data example involving the UK House Price Index data.$

White noise testing is a fundamental problem in time series analysis. Yet it remains largely unsolved for high-dimensional functional time series, despite the growing attention this area has received in recent years, as existing tests are confined to either univariate functional time series or high-dimensional scalar time series. In this paper, we develop a general error-contamination framework for testing white noise in high-dimensional functional time series. We propose a supremum-type test statistic based on cross-autocovariance functions and develop a parametric bootstrap procedure to approximate its null distribution. By imposing a general high-level condition, we derive a new Gaussian approximation result that ensures size control, and establish an asymptotic power guarantee. We then apply our framework to two concrete applications: (i) white noise test for discretely observed functional time series, and (ii) residual-based goodness-of-fit test for functional factor model. For each problem, we verify the corresponding high-level condition to ensure the theoretical validity of our proposed method. Extensive simulations show that our proposed method achieves good finite-sample performance. The practical utility of our proposed method is further illustrated through applications to two real datasets.

This paper develops adaptive procedures for detecting and locating mean changes in high-dimensional time series. Quadratic CUSUM statistics target dense changes, whereas coordinatewise maximum statistics target sparse changes. Two weighting schemes are considered to accommodate both interior and boundary changes. Under general non-Gaussian vector dependence, we establish the limiting distributions, validate the required centering and scaling estimators, and prove asymptotic independence between matched quadratic and maximum statistics. These results justify Cauchy combination tests. We further establish single-change localization and consistent multiple-change recovery using wild binary segmentation. Numerical results illustrate the effectiveness of the proposed methods.

$The twoblock clustering tree (\tbtree) is introduced as a highly interpretable regression tree for multivariate responses. Twoblock trees are deterministic decision trees that have local multivariate linear models as their leaves and use dense or sparse twoblock dimension reduction as local leaf models and in the impurity. The resulting models are both computationally efficient and can be highly interpretable. Beyond proposing the decision tree estimator itself, this paper also introduces an estimator for the twoblock dimension reduced space based on maximizing coskewness, which facilitates identification of non-normal clusters in the data. The tree inherently produces a set of local linear models and is therefore apt to recover peicewise linear regimes, which is illustrated in a simulation. However, two real world data examples illustrate that twoblock trees are also capable of modeling more complexly nonlinear dependencies and can perform on par with black box modeling techniques, such as random forests. At each point, both the twoblock models that generate the splits, as well as the ones in the leaves, can be inspected and interpreted.$

In this work, we study the problem of testing conditional independence between random variables $X$ and $Y$ given a confounder $Z$. The local permutation test (LPT) offers a principled approach to this problem by partitioning the $Z$-space into pre-specified bins, and permuting the $X$ and $Y$ data within each bin, to assess the significance of an observed test statistic. However, when the partitions are pre-fixed, the resulting partition can be poorly balanced, as some bins may contain most of the samples while others contain only a few. This motivates the use of data-adaptive binning strategies, such as equisized bins with a fixed (typically small) number of points. We study this natural and practically important extension of LPT, providing finite-sample bounds on the Type I error for an arbitrary test statistic, providing stronger validity results than previously known. We also show that LPT attains power comparable to the oracle likelihood ratio tests derived from the Neyman-Pearson lemma. Within a linear confounder model class, we further analyze the effect of bin size and demonstrate that constant bin sizes can match the performance of partitions with growing bin-size. These results, further supported by extensive numerical simulations, position the proposed data-adaptive strategy as both practically implementable and statistically efficient.

We study conformal prediction for regression using calibration data with outcomes that are doubly censored (clipped) at known fixed thresholds. We show that existing methods are unsatisfactory in this setting, as they yield intervals that may have higher marginal coverage than desired and yet lose conditional coverage precisely for the easier-to-predict cases whose outcomes are typically fully observed. This reveals that marginal coverage, the usual target of conformal prediction, may not be the ideal goal under clipping. We address this challenge by introducing a new nonconformity score and calibration methods at both ends of this trade-off: one for tight marginal coverage, and a two-step method that prioritizes conditional coverage. We characterize their finite-sample coverage and oracle-like asymptotic behavior under suitable consistency of the underlying model, and we compare them to more direct adaptations of existing approaches.

$Likelihood-based inference in particle physics, and in the physical sciences more broadly, relies on the assumption that the model accurately describes the data. When the model is misspecified, though, standard confidence intervals shrink to zero width with increasing data, producing overconfident and potentially misleading constraints. We propose the well-tempered likelihood, which divides the likelihood-ratio test statistic by a goodness-of-fit (GOF) statistic evaluated at the best-fit point. Under correct specification, the GOF is $\mathcal{O}(1)$ and standard inference is recovered. Under misspecification, both the likelihood and the GOF scale as $\mathcal{O}(N)$ for $N$ data points, so their ratio remains $\mathcal{O}(1)$ and the resulting well-tempered confidence interval self-limits at a floor determined by the model's inadequacy, essentially reducing the effective sample size. In other words, \textit{all models are correct, as long as your dataset is small enough}. We present binned and unbinned formulations of the well-tempered likelihood---the latter based on a classifier two-sample test---and demonstrate our method on a Gaussian example and on a measurement of the strong coupling constant using synthetic electron-positron collisions.$

We propose a Bayesian emulator for extrapolating spatially gridded simulation output across resolution. The method treats each pixel as following a nonlinear resolution-response curve, while linking pixels through Gaussian process priors on the curve parameters to preserve spatial structure and quantify uncertainty. In synthetic experiments designed to mimic resolution-dependent bias, the approach recovers the high-resolution target with competitive or improved accuracy relative to several alternative emulators, particularly in lower-information settings, while maintaining near-nominal interpolative coverage. We also illustrate the method on a radiation-hydrodynamics example from Cassio, where it is used to extrapolate a derived wave-front diagnostic beyond the finest observed simulation. These results suggest that spatially regularized resolution extrapolation can provide a useful statistical tool for studying high-fidelity behavior when direct simulation is expensive.

We develop a theory of nonlinear shrinkage covariance estimation for nonparanormal (Gaussian-copula) models, in which each observed coordinate is an unknown strictly increasing transformation of a latent Gaussian vector. This model accommodates arbitrary marginal skewness and heavy marginal tails while retaining a Gaussian dependence structure, and it is the natural semiparametric setting for heavy-tailed, asymmetric financial returns. Our estimator, marginal-free nonlinear shrinkage (MENS), applies an oracle nonlinear shrinkage function to the eigenvalues of the normal-scores rank-covariance matrix. We give the almost-sure convergence of the empirical spectral distribution of the normal-scores covariance to the generalized Marchenko-Pastur law of Sigma, and asymptotic optimality of MENS among rotation-equivariant estimators under Frobenius loss. We establish a Baik-Ben Arous-Peche phase transition for spiked latent correlations. The MENS attains the robustness of rank-based estimation and the efficiency of nonlinear shrinkage at once within this class. We corroborate the theory with a simulation study that isolates the marginal-invariance property and the spiked transition. In an out-of-sample minimum-variance backtest on S&P 500 stocks, MENS delivers a better-conditioned covariance estimate, lower realized portfolio volatility, and lower turnover than linear shrinkage, illustrating its practical value for high-dimensional allocation and decision-making.

$This paper analyzes spillover effects in spatial (network) models when the neighborhood (adjacency) matrix is contaminated by measurement error from reporting, aggregation, or disclosure imperfections, leading to inconsistent estimation of network effects. We introduce a regularization framework for the latent network that allows for sparse and/or low-rank structure and accommodates potential correlation between measurement errors and outcomes. We propose two estimators: (i) a two-stage procedure that first denoises the adjacency matrix and then incorporates the purified network into a regression analysis, and (ii) a Generalized Method of Moments (GMM) estimator that jointly estimates regression parameters and refines the network structure. We then establish strictly improved consistency rates for the spillover effect estimator relative to naive estimation ignoring measurement error. Simulations demonstrate that, in the presence of noisy networks, our approach reduces the root mean squared error of spillover estimates relative to conventional methods by approximately $50-80\%$. We apply our framework to examine the international spillover of economic growth, and the tax competition across U.S. states, illustrating that denoising might restore Leontief stability and yields improved estimates of spillovers.$

The shape of a planar curve is the geometric information that remains once translation, rotation, scale and reparametrisation are removed and is of interest in many health applications, e.g. in neuroimaging. We propose a deep shape regression model for open planar curves that admits multimodal and high-dimensional covariates. Representing curves as complex-valued functions, we show that the conditional full Procrustes mean is the leading eigenfunction of the conditional covariance. To estimate this covariance surface, we propose a novel deep conditional covariance smoother with modality-specific encoders - e.g. splines for scalar covariates and convolutional networks for images, which classical spline smoothers cannot accommodate. Our model is by construction invariant to the translation, rotation and scaling of the input curves and handles sparsely and irregularly sampled curves. We further provide an algorithm for elastic mean estimation that also removes parametrisation by iterating covariance smoothing, rotational alignment and parametrisation alignment. We illustrate the method on simulated outlines with known conditional mean and multimodal covariates, and give a first application to hippocampal outlines from the ADNI cohort, recovering covariate effects consistent with the literature. Code is available at https://github.com/mpff/dnn-shapes.

Probabilistic extreme event attribution aims to quantify how anthropogenic climate change has altered the likelihood or intensity of a class of extreme events. Existing studies commonly combine evidence from observational products and climate-model ensembles by first estimating attribution measures, such as probability ratios or intensity changes, for each data source and then synthesizing the resulting estimates. We critically assess this approach, identify potential shortcomings of a respective benchmark procedure from the literature, and propose both targeted modifications and a new parameter-level synthesis method. The latter combines estimates of the underlying nonstationary distributional regression parameters, thereby enabling inference across multiple event thresholds and counterfactual climate conditions. In controlled simulation studies, the proposed modifications substantially improve upon the benchmark procedure, while parameter-level synthesis provides competitive overall performance. The practical usefulness is illustrated through a case study of the heavy precipitation associated with Storm Boris in September 2024.

In this paper we review recent advances in statistical methods for the
evaluation of the heterogeneity of treatment effects (HTE), including subgroup
identification and estimation of individualized treatment regimens, from
randomized clinical trials and observational studies. We identify several types
of approaches using the features introduced in Lipkovich, Dmitrienko and
D'Agostino (2017) that distinguish the recommended principled methods from
basic methods for HTE evaluation that typically rely on rules of thumb and
general guidelines (the methods are often referred to as common practices). We
discuss the advantages and disadvantages of various principled methods as well
as common measures for evaluating their performance. We use simulated data and
a case study based on a historical clinical trial to illustrate several new
approaches to HTE evaluation.

Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability distribution. In this paper we propose goodness-of-fit statistics for the multivariate Student and multivariate Pearson type II distributions, based on the maximum entropy principle and a class of estimators for Renyi entropy based on nearest neighbour distances. We prove the L2-consistency of these statistics using results on the subadditivity of Euclidean functionals on nearest neighbour graphs, and investigate their rate of convergence and asymptotic distribution using Monte Carlo methods.

arXiv:2408.02573v1 Announce Type: new
Abstract: This paper develops sharp testable implications for Tobit and IV-Tobit models' identifying assumptions: linear index specification, (joint) normality of latent errors, and treatment (instrument) exogeneity and relevance. The new sharp testable equalities can detect all possible observable violations of the identifying conditions. We propose a testing procedure for the model's validity using existing inference methods for intersection bounds. Simulation results suggests proper size for large samples and that the test is powerful to detect large violation of the exogeneity assumption and violations in the error structure. Finally, we review and propose new alternative paths to partially identify the parameters of interest under less restrictive assumptions.

In frequency domain analysis for spatial data, spectral averages based on the periodogram often play an important role in understanding spatial covariance structure, but also have complicated sampling distributions due to complex variances from aggregated periodograms. In order to nonparametrically approximate these sampling distributions for purposes of inference, resampling can be useful, but previous developments in spatial bootstrap have faced challenges in the scope of their validity, specifically due to issues in capturing the complex variances of spatial spectral averages. As a consequence, existing frequency domain bootstraps for spatial data are highly restricted in application to only special processes (e.g. Gaussian) or certain spatial statistics. To address this limitation and to approximate a wide range of spatial spectral averages, we propose a practical hybrid-resampling approach that combines two different resampling techniques in the forms of spatial subsampling and spatial bootstrap. Subsampling helps to capture the variance of spectral averages while bootstrap captures the distributional shape. The hybrid resampling procedure can then accurately quantify uncertainty in spectral inference under mild spatial assumptions. Moreover, compared to the more studied time series setting, this work fills a gap in the theory of subsampling/bootstrap for spatial data regarding spectral average statistics.

The R package glmSTARMA implements autoregressive models for spatio-temporal data at fixed locations, with time-invariant spatial dependency structure. We rely on generalized linear models methodology and unify several approaches for the analysis of spatial count time series. Such models allow the (conditional) mean of the response to depend on past observations, lagged (conditional) expectations, and covariates. The response can be a continuous or a discrete random variable. Additionally, the package develops inference for double generalized linear models, allowing the dispersion parameter(s) of the marginal distributions to be modeled similarly to the mean process. This is a new capability which introduces, for example, spatio-temporal volatility models, such as space-time GARCH processes, and count time series models with spatio-temporal overdispersion and underdispersion. We provide functions for model estimation, simulation, inference, and prediction. Its use is illustrated by data examples.

Online change-point detection in high-dimensional nonlinear time series faces two challenges. The underlying distributions are difficult to model, and state changes are difficult to characterize. We propose persistent Laplacian cumulative sum (PL-CUSUM) to address these challenges. PL-CUSUM maps delay-embedded sliding windows to point clouds. It extracts persistent Betti vectors and the positive spectra of persistent Laplacians from the same Vietoris-Rips filtration. A ridge-whitened projection converts these features into a scalar score. Page's CUSUM recursion then accumulates this score over time. The positive spectra capture within-scale connectivity and geometric information that persistent Betti vectors do not record. Under a finite-support local model, we prove that the oracle upper bound on detection delay and a local minimax lower bound have the same order. This common order is the logarithm of the average run length constraint divided by the squared ridge-whitened separation. We also establish finite-horizon false-alarm and expected-delay bounds for plug-in whitened scores under weak dependence within each state. The method has two phases. Phase I estimates the projection parameters, selects the feature configuration, and calibrates the control limit. Phase II updates the resulting CUSUM statistic online. Experiments on simulated and real monitoring data show stable false-alarm control and competitive detection performance.

Change-plane regression represents treatment effect heterogeneity through an interpretable rule that assigns patients to two groups according to whether a linear score of baseline covariates crosses a threshold. Although easy to communicate, likelihood-based inference for the hard threshold is nonregular, invalidating standard large-sample approximations. We develop a Bayesian framework that replaces the sharp indicator with a smooth probit gate at a declared smoothing scale and treats the smoothed subgroup rule as the reported estimand. At a fixed smoothing scale, the posterior satisfies a misspecified Bernstein--von Mises theorem centered at the smoothed rule. Under a vanishing smoothing schedule, the posterior learns the boundary faster than the parametric rate, while within an explicit schedule window the regression block and treatment-effect contrast satisfy a Bernstein--von Mises theorem centered at the hard-threshold values with known-subgroup oracle efficiency. Thus, effect inference pays no first-order price for regularization. A decision-theoretic reporting protocol with consistency guarantees separates evidence of heterogeneity from reporting a boundary. Computation uses latent-variable augmentation, a great-circle elliptical slice sampler, and a normalized horseshoe prior. Simulations and an application to the PREMIER trial illustrate the method.

Two misunderstandings, frequently arising in Bayesian predictive inference, are discussed. The first deals with the data generating mechanism, while the second consists in overestimating the role played by asymptotic exchangeability. Some consequences of such misunderstandings are highlighted through examples.

$Transport-based quantiles extend univariate quantiles to multivariate distributions via optimal transport. We study the influence function of the transport quantile map $\mathbf{Q}_P$, defined as the optimal transport map pushing a fixed reference measure $\mu$ forward to a target distribution $P$. For the Huber contamination $P_t=(1-t)P+t\delta_{x_0}$, we prove that the first-order limit $\mathbf{I}(x_0;\mathbf{Q}_P(z)) := \lim_{t\downarrow 0} [\mathbf{Q}_{(1-t)P+t\delta_{x_0}}(z)-\mathbf{Q}_P(z)]/t$ exists whenever $x_0\ne \mathbf{Q}_P(z)$ and characterize it uniquely. Specifically, $\mathbf{I}(x_0;\mathbf{Q}_P(z))=\nabla G_{x_0}(z)$, where $G_{x_0}$ is characterized by a uniformly elliptic equation with a Dirac source and a Neumann boundary condition. In every dimension $d\ge 2$, this influence function has a pole-type singularity. For fixed $z\in\operatorname{int}(\Omega_\mu)$, it remains bounded when $\mathbf{F}_P(x_0)$ stays away from $z$, where $\mathbf{F}_P=\mathbf{Q}_P^{-1}$ is the transport-based distribution function, but diverges as $x_0\to\mathbf{Q}_P(z)$, equivalently as $\mathbf{F}_P(x_0)\to z$. In fact, $\|\mathbf{I}(x_0;\mathbf{Q}_P(z))\|\asymp\|z-\mathbf{F}_P(x_0)\|^{-(d-1)}$. This contrasts with the bounded influence function of univariate quantiles and implies that $\mathbf{I}(X;\mathbf{Q}_P(z))$, for $X\sim P$, has infinite second moment. Numerical experiments further suggest that empirical transport quantiles may exhibit stable-type non-Gaussian fluctuations.$

Sufficient dimension reduction seeks a low-dimensional covariate representation that preserves the conditional law of a response. We introduce SDR-COT, which represents that law by conditional optimal transport from an independent reference response. On separable Hilbert spaces, sufficiency forces the response component of the optimal triangular map to factor through the reduction. For quadratic cost, the induced interpolation has a Borel current-state velocity on every truncated time interval, without global injectivity of the terminal map, and this velocity has the same factorisation. These results motivate a conditional-flow-matching criterion. For linear reductions, we prove consistency using a suitably tuned relaxed empirical coupling. Euclidean responses are treated through slicewise Caffarelli bounds; Hilbert-valued responses are treated through Gaussian Sobolev regularity, interpolation compression and uniqueness of a Gaussian continuity equation. Numerical studies with Euclidean and functional data show competitive performance, especially when sufficient information is not solely contained in the conditional mean.

Uncertainty quantification (UQ) is essential to experimental mechanics, but has become particularly relevant in computational mechanics, manifesting in two fundamental problem types: forward and inverse problems. The former addresses how input uncertainties propagate to the quantities of interest, whereas the latter aims to infer unknown parameters from experimental observations or simulations. Since efficient propagation typically requires a prohibitive number of evaluations to compute marginal output distributions, the development of fast, data-driven surrogate models becomes necessary. Thus, we can distinguish between two inverse tasks: (i) the identification and calibration of input uncertainties, and (ii) the construction of surrogates, a methodology collectively referred to as surrogate-based UQ. Building on probabilistic reasoning and the concept of partial belief, we demonstrate that Bayesian probability theory provides a unified theoretical framework for addressing both problem types. We further show that Bayesian inference allows for the seamless incorporation of essential subproblems, including model selection for identifying the most probable model specifications and experimental design for optimizing data collection by identifying experiments or simulations that maximize expected information gain about parameters, among others such as connections to sensitivity analysis or the use of special priors like random fields. While this theoretical framework is presented for general mechanical problems, particular emphasis is placed on biomechanics, where variability and uncertainty is especially pronounced due to inherent biological heterogeneity, patient-specific variability, and noisy data.

$Given observations $\mathbf x=(x_1,\dots,x_n)$, Gaffke (2005) defined \[ K_n(\mathbf x)=\mathbb{P}_{\mathbf D}\!\left\{\sum_{i=1}^n x_iD_i\le 1\right\}, \qquad (D_0,D_1,\ldots,D_n)\sim\mathrm{Dirichlet}(1,\ldots,1), \] and conjectured that it is a $p$-value whenever the inputs are independent e-values. Recently, Vlassis and Thomas (2026) proved this conjecture. Inverting the tests for observations in $[0,1]$ gives the confidence interval studied by Learned-Miller and Thomas (2020), which reduces to Clopper--Pearson for Bernoulli data. We give a finite- and large-sample account of Gaffke's test and interval. First, for every $\mathbf x\in[0,\infty)^n$ and every elementary symmetric polynomial $e_k$, $ K_n(\mathbf x)e_k(\mathbf x)\le {n\choose k}, $ so the Gaffke $p$-value never larger than the SymPol $p$-value of Ming et al. (2026). However, Gaffke's p-value is inadmissible. For $n=2$, we construct a valid rule that is strictly smaller on mixed configurations and is the unique admissible rule that dominates $K_2$. A neutral-face extension proves inadmissibility of $K_n$ for every $n\ge2$. If one independent uniform random variable is allowed, there is an even simpler full-dimensional improvement: on the upper orthant, where $K_n(\mathbf x)=1/\prod_i x_i$, replace it by $U/\prod_i x_i$. The equal-tail Gaffke confidence interval $I_n$ is nevertheless first-order asymptotically efficient: for iid observations on $[0,1]$ with unknown variance $\sigma^2>0$, \[ \sqrt n\,\operatorname{Width}(I_n)\longrightarrow 2\sigma z_{1-\alpha/2}\qquad\text{almost surely}. \] Our simulations also find that, among a variety of bounded-mean intervals considered, the Gaffke interval is the shortest, including comparisons with a recent empirical Berry--Esseen procedure having the same first-order Gaussian target.$

We develop an exact finite-population stochastic framework for SIR epidemics evolving under Markovian switching between intervention regimes. The epidemic state is augmented by a finite phase component, allowing transmission, recovery, and direct immunity-acquisition rates to depend on the active regime. Phase-transition intensities may depend on the current epidemic state, so that policy escalation can react to the number of infectious individuals. Exploiting the monotonicity of the susceptible compartment, we derive level-wise recursions for the joint Laplace--Stieltjes transform and probability generating function of the extinction time and the number of infections generated before extinction. These recursions yield the infection-count distribution, conditional extinction-time transforms, and mixed moments linking epidemic duration and infection burden, while replacing a large global linear system with small phase-level solves. The framework is illustrated using weekly mpox incidence data from Luxembourg. A baseline one-phase SIR model is calibrated by maximum likelihood under a Poisson observation model. The calibrated baseline is then used for conditional comparisons of fixed control regimes, early versus delayed strict intervention, vaccination-supported control, and state-dependent escalation. The results show how switching mechanisms affect both the total number of infected individuals and the extinction time, including their dispersion. Since the switching mechanisms are specified rather than estimated from the intervention history, the results are conditional model-based comparisons rather than estimates of the historical effects of interventions in Luxembourg.

$This paper introduces a class of observation-driven models whose systematic component includes a tempered fractional differencing term. This specification generalizes long-range dependent models based on the fractional differencing operator, enabling a more general and robust model specification while offering theoretical advantages. We propose a partial maximum likelihood approach for parameter estimation and address hypothesis testing, confidence intervals, goodness-of-fit assessment, and both in-sample and out-of-sample forecasting. A Monte Carlo simulation study evaluates the finite-sample performance of the proposed estimation method, and an empirical application illustrates the model's practical utility.$