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We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert-Schmidt norm of the usual empirical estimator of normalized…

Statistics Theory · Mathematics 2022-11-11 Terence Kevin Manfoumbi Djonguet , Guy Martial Nkiet

We consider three models (elliptic, flat and hyperbolic) of Gaussian random analytic functions distinguished by invariance of their zeroes distribution. Asymptotic normality is proven for smooth functionals (linear statistics) of the set of…

Complex Variables · Mathematics 2007-05-23 Mikhail Sodin , Boris Tsirelson

Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…

Statistics Theory · Mathematics 2021-10-06 Lan Gao , Yingying Fan , Jinchi Lv , Qi-Man Shao

To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied in practice before more specialized analysis is carried out. Although a plethora of aggregate tests…

Statistics Theory · Mathematics 2024-05-08 Anders Bredahl Kock , David Preinerstorfer

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…

Machine Learning · Computer Science 2025-11-03 Pierre-François Massiani , Christian Fiedler , Lukas Haverbeck , Friedrich Solowjow , Sebastian Trimpe

We study a novel class of affine invariant and consistent tests for multivariate normality. The tests are based on a characterization of the standard $d$-variate normal distribution by means of the unique solution of an initial value…

Statistics Theory · Mathematics 2020-07-07 Bruno Ebner , Norbert Henze , David Strieder

We present the asymptotic distribution for two-sided tests based on the profile likelihood ratio with lower and upper boundaries on the parameter of interest. This situation is relevant for branching ratios and the elements of unitary…

Data Analysis, Statistics and Probability · Physics 2012-10-26 Glen Cowan , Kyle Cranmer , Eilam Gross , Ofer Vitells

We provide a means of computing and estimating the asymptotic distributions of statistics based on an outer minimization of an inner maximization. Such test statistics, which arise frequently in moment models, are of special interest in…

Econometrics · Economics 2024-04-17 Isaac Loh

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…

Statistics Theory · Mathematics 2009-09-29 Lawrence D. Brown , M. Levine

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

Machine Learning · Computer Science 2013-02-21 George H. John , Pat Langley

In this article we study the field of Hilbertian metrics and positive definit (pd) kernels on probability measures, they have a real interest in kernel methods. Firstly we will make a study based on the Alpha-Beta-divergence to have a…

Methodology · Statistics 2018-09-18 Mactar Ndaw , Macoumba Ndour , Papa Ngom

The widespread adoption of the \emph{maximum mean discrepancy} (MMD) in goodness-of-fit testing has spurred extensive research on its statistical performance. However, recent studies indicate that the inherent structure of MMD may constrain…

Methodology · Statistics 2025-11-11 Shiwei Sang , Shao-Bo Lin , Xuehu Zhu

This paper establishes a formal connection between finite-sample and asymptotically minimax robust hypothesis testing under distributional uncertainty. It is shown that, whenever a finite-sample minimax robust test exists, it coincides with…

Statistics Theory · Mathematics 2026-02-24 Gökhan Gül

Let $X_1,X_2, \ldots$ be independent and identically distributed random elements taking values in a separable Hilbert space $\mathbb{H}$. With applications for functional data in mind, $\mathbb{H}$ may be regarded as a space of…

Statistics Theory · Mathematics 2019-10-25 Norbert Henze , M. Dolores Jiménez--Gamero

This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…

Methodology · Statistics 2025-11-05 Yiou Li , Lulu Kang

We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test…

Information Theory · Computer Science 2021-02-08 Shengyu Zhu , Biao Chen , Zhitang Chen , Pengfei Yang

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

We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has…

Machine Learning · Computer Science 2021-01-11 Junhyung Park , Krikamol Muandet

In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…

Statistics Theory · Mathematics 2020-05-14 Noirrit Kiran Chandra , Sourabh Bhattacharya

Discontinuity in density functions is of economic importance and interest. For instance, in studies on regression discontinuity designs, discontinuity in the density of a running variable suggests violation of the no-manipulation…

Statistics Theory · Mathematics 2016-08-02 Benedikt Funke , Masayuki Hirukawa