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After rejecting the null hypothesis in the analysis of variance, the next step is to make the pairwise comparisons to find out differences in means. The purpose of this paper is threefold. The foremost aim is to suggest expression for…

Methodology · Statistics 2023-06-22 Elsayed A. H. Elamir

Comparing conditional distributions is a fundamental challenge in statistics and machine learning, with applications across a wide range of domains. While proposed methods for measuring discrepancies using kernel embeddings of distributions…

Machine Learning · Statistics 2026-05-05 Peter Moskvichev , Siu Lun Chau , Dino Sejdinovic

We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the…

When studying treatment effects in multilevel studies, investigators commonly use (semi-)parametric estimators, which make strong parametric assumptions about the outcome, the treatment, and/or the correlation structure between study units…

Methodology · Statistics 2022-05-12 Chan Park , Hyunseung Kang

Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with…

Statistics Theory · Mathematics 2007-06-13 Chong Gu , Ping Ma

Randomized trials are considered the gold standard for estimating causal effects. Trial findings are often used to inform policy and programming efforts, yet their results may not generalize well to a relevant target population due to…

With limited resources, scientific inquiries must be prioritized for further study, funding, and translation based on their practical significance: whether the effect size is large enough to be meaningful in the real world. Doing so must…

Methodology · Statistics 2022-05-27 Bruce A. Corliss , Yaotian Wang , Heman Shakeri , Philip E. Bourne

We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD…

In cluster-randomized trials, generalized linear mixed models and generalized estimating equations have conventionally been the default analytic methods for estimating the average treatment effect as routine practice. However, recent…

Methodology · Statistics 2025-09-19 Fan Li , Jiaqi Tong , Xi Fang , Chao Cheng , Brennan C. Kahan , Bingkai Wang

Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence and statistical estimation rates are well-understood for…

Machine Learning · Statistics 2020-07-31 Lu Yu , Krishnakumar Balasubramanian , Stanislav Volgushev , Murat A. Erdogdu

In this paper, a Bayesian approach is developed for simultaneously comparing multiple experimental treatments with a common control treatment in an exploratory clinical trial. The sample size is set to ensure that, at the end of the study,…

Statistics Theory · Mathematics 2019-11-14 John Whitehead , Faye Cleary , Amanda Turner

In this paper, we address the normal mean inference problem, which involves testing multiple means of normal random variables with heteroscedastic variances. Most existing empirical Bayes methods for this setting are developed under…

Methodology · Statistics 2026-01-01 Kwangok Seo , Johan Lim , Kaiwen Wang , Dohwan Park , Shota Katayama , Xinlei Wang

Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…

Machine Learning · Statistics 2026-04-21 Antoine Chatalic , Marco Letizia , Nicolas Schreuder , Lorenzo Rosasco

Structural nested mean models (SNMMs) are a principled approach to estimate the treatment effects over time. A particular strength of SNMMs is to break the joint effect of treatment sequences over time into localized, time-specific ``blip…

Machine Learning · Statistics 2025-11-19 Haorui Ma , Dennis Frauen , Stefan Feuerriegel

Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…

Machine Learning · Computer Science 2013-05-03 Somayeh Danafar , Paola M. V. Rancoita , Tobias Glasmachers , Kevin Whittingstall , Juergen Schmidhuber

Inference in models where the parameter is defined by moment inequalities is of interest in many areas of economics. This paper develops a new method for improving the performance of generalized moment selection (GMS) testing procedures in…

Econometrics · Economics 2020-08-26 Rami V. Tabri , Christopher D. Walker

A primary concern of public health researchers involves identifying and quantifying heterogeneous exposure effects across population subgroups. Understanding the magnitude and direction of these effects on a given scale provides researchers…

Applications · Statistics 2024-01-30 Michael Cheung , Anna Dimitrova , Tarik Benmarhnia

Regression Discontinuity Design (RDD) is a popular framework for estimating a causal effect in settings where treatment is assigned if an observed covariate exceeds a fixed threshold. We consider estimation and inference in the common…

Statistics Theory · Mathematics 2025-04-16 Kevin Tao , Y. Samuel Wang , David Ruppert

In empirical studies with time-to-event outcomes, investigators often leverage observational data to conduct causal inference on the effect of exposure when randomized controlled trial data is unavailable. Model misspecification and lack of…

Methodology · Statistics 2023-05-05 Shenbo Xu , Bang Zheng , Bowen Su , Stan Finkelstein , Roy Welsch , Kenney Ng , Ioanna Tzoulaki , Zach Shahn

Random-effects meta-analyses are used to combine evidence of treatment effects from multiple studies. Since treatment effects may vary across trials due to differences in study characteristics, heterogeneity in treatment effects between…

Methodology · Statistics 2017-07-10 Tim Friede , Christian Röver , Simon Wandel , Beat Neuenschwander
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