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Rejecting the null hypothesis in two-sample testing is a fundamental tool for scientific discovery. Yet, aside from concluding that two samples do not come from the same probability distribution, it is often of interest to characterize how…

Statistics Theory · Mathematics 2021-09-08 Boris Landa , Rihao Qu , Joseph Chang , Yuval Kluger

This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…

Optimization and Control · Mathematics 2026-02-05 Chung-Han Hsieh

In this paper we develop rate--optimal estimation procedures in the problem of estimating the $L_p$--norm, $p\in (0, \infty)$ of a probability density from independent observations. The density is assumed to be defined on $R^d$, $d\geq 1$…

Statistics Theory · Mathematics 2020-08-26 Alexander Goldenshluger , Oleg Lepski

The paper deals with the problem of nonparametric estimating the $L_p$--norm, $p\in (1,\infty)$, of a probability density on $R^d$, $d\geq 1$ from independent observations. The unknown density %to be estimated is assumed to belong to a ball…

Statistics Theory · Mathematics 2020-08-26 Alexander Goldenshluger , Oleg Lepski

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

Machine Learning · Computer Science 2026-03-10 Davide Maran , Marcello Restelli

We propose a class of locally and asymptotically optimal tests, based on multivariate ranks and signs for the homogeneity of scatter matrices in $m$ elliptical populations. Contrary to the existing parametric procedures, these tests remain…

Statistics Theory · Mathematics 2008-12-18 Marc Hallin , Davy Paindaveine

The design of optimal test statistics is a key task in frequentist statistics and for a number of scenarios optimal test statistics such as the profile-likelihood ratio are known. By turning this argument around we can find the profile…

Methodology · Statistics 2022-03-25 Lukas Heinrich

The paper deals with minimax optimal statistical tests for two composite hypotheses, where each hypothesis is defined by a non-parametric uncertainty set of feasible distributions. It is shown that for every pair of uncertainty sets of the…

Statistics Theory · Mathematics 2018-04-17 Michael Fauss , Abdelhak M. Zoubir , H. Vincent Poor

We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections of the input data through functional…

Statistics Theory · Mathematics 2013-02-12 Nadine Hilgert , André Mas , Nicolas Verzelen

Motivated by applications to goodness of fit testing, the empirical likelihood approach is generalized to allow for the number of constraints to grow with the sample size and for the constraints to use estimated criteria functions. The…

Statistics Theory · Mathematics 2013-07-24 Hanxiang Peng , Anton Schick

We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically…

Statistics Theory · Mathematics 2013-11-07 Jinyuan Chang , Cheng Yong Tang , Yichao Wu

This paper considers the problem of multi-sample nonparametric comparison of counting processes with panel count data, which arise naturally when recurrent events are considered. Such data frequently occur in medical follow-up studies and…

Statistics Theory · Mathematics 2009-04-21 N. Balakrishnan , Xingqiu Zhao

We consider the problem of detecting a community of densely connected vertices in a high-dimensional bipartite graph of size $n_1 \times n_2$. Under the null hypothesis, the observed graph is drawn from a bipartite Erd\H{o}s-Renyi…

Statistics Theory · Mathematics 2025-05-27 Julien Chhor , Parker Knight

Two new goodness of fit tests for the Pareto type-I distribution for complete and right censored data are proposed using fixed point characterization based on Steins type identity. The asymptotic distributions of the test statistics under…

Methodology · Statistics 2024-08-30 Avhad Ganesh Vishnu , Ananya Lahiri , Sudheesh K. Kattumannil

We study the problem of nonparametric two-sample testing using the sliced Wasserstein (SW) distance. While prior theoretical and empirical work indicates that the SW distance offers a promising balance between strong statistical guarantees…

Machine Learning · Statistics 2025-11-03 Binh Thuan Tran , Nicolas Schreuder

Estimating the mixing density of a latent mixture model is an important task in signal processing. Nonparametric maximum likelihood estimation is one popular approach to this problem. If the latent variable distribution is assumed to be…

Methodology · Statistics 2024-03-01 Shijie Wang , Minsuk Shin , Ray Bai

We consider the problem of testing the hypothesis that the parameter of linear regression model is 0 against an s-sparse alternative separated from 0 in the l2-distance. We show that, in Gaussian linear regression model with p < n, where p…

Statistics Theory · Mathematics 2018-10-11 Alexandra Carpentier , Olivier Collier , Laëtitia Comminges , Alexandre B. Tsybakov , Yuhao Wang

Missing covariates are not uncommon in capture-recapture studies. When covariate information is missing at random in capture-recapture data, an empirical full likelihood method has been demonstrated to outperform…

Methodology · Statistics 2025-07-15 Yang Liu , Yukun Liu , Pengfei Li , Riquan Zhang

We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently we estimate the causal effect of a treatment,…

Statistics Theory · Mathematics 2020-09-23 Kolyan Ray , Aad van der Vaart

This work studies an experimental design problem where {the values of a predictor variable, denoted by $x$}, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to…

Statistics Theory · Mathematics 2023-05-03 David Azriel