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The problem of testing equality of the entire second order structure of two independent functional linear processes is considered. A fully functional $L^2$-type test is developed which evaluates, over all frequencies, the Hilbert-Schmidt…

Methodology · Statistics 2020-04-15 Anne Leucht , Efstathios Paparoditis , Theofanis Sapatinas

We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and…

Methodology · Statistics 2023-02-24 Xiaoyu Hu , Jing Lei

Deep neural two-sample tests have recently shown strong power for detecting distributional differences between groups, yet their black-box nature limits interpretability and practical adoption in biomedical analysis. Moreover, most existing…

Computer Vision and Pattern Recognition · Computer Science 2026-02-06 Masoumeh Javanbakhat , Piotr Komorowski , Dilyara Bareeva , Wei-Chang Lai , Wojciech Samek , Christoph Lippert

We consider the problem of comparing probability densities between two groups. A new probabilistic tensor product smoothing spline framework is developed to model the joint density of two variables. Under such a framework, the probability…

Methodology · Statistics 2021-01-13 Xin Xing , Zuofeng Shang , Pang Du , Ping Ma , Wenxuan Zhong , Jun S. Liu

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

This paper considers the problem of comparing two processes with panel data. A nonparametric test is proposed for detecting a monotone change in the link between the two process distributions. The test statistic is of CUSUM type, based on…

Statistics Theory · Mathematics 2011-05-04 Denys Pommeret , Mohamed Boutahar , Badih Ghattas

We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some…

Machine Learning · Statistics 2020-07-01 Wittawat Jitkrittum , Heishiro Kanagawa , Bernhard Schölkopf

We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…

Statistics Theory · Mathematics 2022-11-03 Sherzod M Mirakhmedov

Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…

Statistics Theory · Mathematics 2017-07-25 Abhik Ghosh , Ayanendranath Basu

Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behavior of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the…

Statistics Theory · Mathematics 2024-10-31 Jian Yan , Xianyang Zhang

Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…

Methodology · Statistics 2019-10-08 Vitaliy Oryshchenko , Richard J. Smith

We develop a nonparametric two-sample test for distributions supported on the cone of symmetric positive definite matrices. The procedure relies on the Wishart kernel density estimator (KDE) introduced by Belzile et al. (2025), whose…

Statistics Theory · Mathematics 2026-03-17 Frédéric Ouimet

We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a…

Econometrics · Economics 2020-09-18 Bas Werker , Bo Zhou

The kernel Maximum Mean Discrepancy~(MMD) is a popular multivariate distance metric between distributions that has found utility in two-sample testing. The usual kernel-MMD test statistic is a degenerate U-statistic under the null, and thus…

Methodology · Statistics 2025-09-16 Shubhanshu Shekhar , Ilmun Kim , Aaditya Ramdas

Given $n$ observations from two balanced classes, consider the task of labeling an additional $m$ inputs that are known to all belong to \emph{one} of the two classes. Special cases of this problem are well-known: with complete knowledge of…

Machine Learning · Statistics 2023-11-27 Patrik Róbert Gerber , Tianze Jiang , Yury Polyanskiy , Rui Sun

Data objects taking value in a general metric space have become increasingly common in modern data analysis. In this paper, we study two important statistical inference problems, namely, two-sample testing and change-point detection, for…

Methodology · Statistics 2023-07-11 Feiyu Jiang , Changbo Zhu , Xiaofeng Shao

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

A new goodness-of-fit test for normality in high-dimension (and Reproducing Kernel Hilbert Space) is proposed. It shares common ideas with the Maximum Mean Discrepancy (MMD) it outperforms both in terms of computation time and applicability…

Statistics Theory · Mathematics 2014-04-14 Jérémie Kellner , Alain Celisse

We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and…

Statistics Theory · Mathematics 2023-05-11 Fengnan Gao , Tengyao Wang

We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…

Statistics Theory · Mathematics 2017-05-09 Taras Bodnar , Stepan Mazur , Edward Ngailo , Nestor Parolya