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We propose a family of tests of the validity of the assumptions underlying independent component analysis methods. The tests are formulated as L2-type procedures based on characteristic functions and involve weights; a proper choice of…

Methodology · Statistics 2024-04-12 Marc Hallin , Simos G. Meintanis , Klaus Nordhausen

In this paper, we propose a new test for checking the parametric form of the conditional variance based on distance covariance in nonlinear and nonparametric regression models. Inherit from the nice properties of distance covariance, our…

Methodology · Statistics 2022-05-19 Yue Hu , Haiqi Li , Falong Tan

We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero…

Statistics Theory · Mathematics 2020-02-28 Bruno Ebner

The assumption of normality has underlain much of the development of statistics, including spatial statistics, and many tests have been proposed. In this work, we focus on the multivariate setting and first review the recent advances in…

Methodology · Statistics 2022-05-18 Wanfang Chen , Marc G. Genton

This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the…

Statistics Theory · Mathematics 2019-02-12 Natsumi Makigusa , Kanta Naito

This short note considers the problem of testing the null hypothesis that the mean values of two multivariate normal variables are proportional. We show that the usual likelihood ratio $\chi^2$-test is valid non-asymptotically. Our proof…

Statistics Theory · Mathematics 2021-03-10 Etaash Katiyar , Qingyuan Zhao

We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein's identity with the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic…

Machine Learning · Statistics 2016-07-04 Qiang Liu , Jason D. Lee , Michael I. Jordan

Many important problems in psychology and biomedical studies require testing for overdispersion, correlation and heterogeneity in mixed effects and latent variable models, and score tests are particularly useful for this purpose. But the…

Statistics Theory · Mathematics 2007-06-13 Hongtu Zhu , Heping Zhang

Given a random sample of observations, mixtures of normal densities are often used to estimate the unknown continuous distribution from which the data come. Here we propose the use of this semiparametric framework for testing symmetry about…

Methodology · Statistics 2012-04-23 Silvia Bacci , Francesco Bartolucci

In this paper we propose a new test for the hypothesis of a constant coefficient of variation in the common nonparametric regression model. The test is based on an estimate of the $L^2$-distance between the square of the regression function…

Statistics Theory · Mathematics 2008-09-30 H. Dette , G. Wieczorek

From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop…

Methodology · Statistics 2022-02-16 Steffen Betsch , Bruno Ebner , Franz Nestmann

Under a multinormal distribution with arbitrary unknown covariance matrix, the main purpose of this paper is to propose a framework to achieve the goal of reconciliation of Bayesian, frequentist and Fisherian paradigms for the problems of…

Statistics Theory · Mathematics 2019-12-24 Ming-Tien Tsai

In a recent paper, Gaunt 2020 extended Stein's method to limit distributions that can be represented as a function $g:\mathbb{R}^d\rightarrow\mathbb{R}$ of a centered multivariate normal random vector $\Sigma^{1/2}\mathbf{Z}$ with…

Probability · Mathematics 2022-09-21 Robert E. Gaunt , Heather Sutcliffe

In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…

Statistics Theory · Mathematics 2020-06-08 Ilmun Kim

In the first part of the paper we use a new Fourier technique to obtain a Stein characterizations for random variables in the second Wiener chaos. We provide the connection between this result and similar conclusions that can be derived…

Probability · Mathematics 2016-01-14 Benjamin Arras , Ehsan Azmoodeh , Guillaume Poly , Yvik Swan

The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…

Statistics Theory · Mathematics 2022-09-12 Sherzod M. Mirakhmedov

We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability in the regression parameters against the alternative of a break at an unknown time. We derive the extreme value…

Statistics Theory · Mathematics 2008-10-23 Alexander Aue , Lajos Horváth , Marie Hušková , Piotr Kokoszka

Most normality tests in the literature are performed for scalar and independent samples. Thus, they become unreliable when applied to colored processes, hampering their use in realistic scenarios.We focus on Mardia's multivariate kurtosis,…

Methodology · Statistics 2022-03-02 Sara Elbouch , Olivier Michel , Pierre Comon

It has been a long history in testing whether a mean vector with a fixed dimension has a specified value. Some well-known tests include the Hotelling $T^2$-test and the empirical likelihood ratio test proposed by Owen [Biometrika 75 (1988)…

Methodology · Statistics 2014-05-21 Liang Peng , Yongcheng Qi , Fang Wang

Using the fact that some depth functions characterize certain family of distribution functions, and under some mild conditions, distribution of the depth is continuous, we have constructed several new multivariate goodness of fit tests…

Statistics Theory · Mathematics 2024-05-14 Rahul Singh , Subhajit Dutta , Neeraj Misra