English
Related papers

Related papers: Tests for multivariate normality -- a critical rev…

200 papers

We investigate the likelihood ratio test for a large block-diagonal covariance matrix with an increasing number of blocks under the null hypothesis. While so far the likelihood ratio statistic has only been studied for normal populations,…

Statistics Theory · Mathematics 2024-08-01 Nina Dörnemann

The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n \to \infty$. Based on this…

Methodology · Statistics 2021-09-15 Jiaxin Qiu , Zeng Li , Jianfeng Yao

We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture…

Methodology · Statistics 2024-03-13 Nicoletta D'Angelo , Giada Adelfio , Jorge Mateu , Ottmar Cronie

This article inspects whether a multivariate distribution is different from a specified distribution or not, and it also tests the equality of two multivariate distributions. In the course of this study, a graphical tool-kit using…

Methodology · Statistics 2024-08-19 Pratim Guha Niyogi , Subhra Sankar Dhar

In this paper, we investigate the testing problem that the spectral density matrices of several, not necessarily independent, stationary processes are equal. Based on an $L_2$-type test statistic, we propose a new nonparametric approach,…

Statistics Theory · Mathematics 2015-06-03 Carsten Jentsch , Markus Pauly

Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this paper, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data…

Statistics Theory · Mathematics 2023-06-09 Yiting Chen , Wei Lin , Xiaoping Shi

We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…

Methodology · Statistics 2020-02-25 Steffen Betsch , Bruno Ebner

The large-sample behavior of non-degenerate multivariate $U$-statistics of arbitrary degree is investigated under the assumption that their kernel depends on parameters that can be estimated consistently. Mild regularity conditions are…

Statistics Theory · Mathematics 2025-07-22 Alain Desgagné , Christian Genest , Frédéric Ouimet

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

In this article, we propose a class of $L_q$-norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model…

Statistics Theory · Mathematics 2023-03-16 Yangfan Zhang , Runmin Wang , Xiaofeng Shao

Although unbiasedness is a basic property of a good test, many tests on vector parameters or scalar parameters against two-sided alternatives are not finite-sample unbiased. This was already noticed by Sugiura [Ann. Inst. Statist. Math. 17…

Statistics Theory · Mathematics 2012-03-05 Jana Jurečková , Jan Kalina

Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…

Methodology · Statistics 2021-02-01 Mingao Yuan , Qian Wen

A variety of estimators for the parameters of the Generalized Pareto distribution, the approximating distribution for excesses over a high threshold, have been proposed, always assuming the underlying data to be independent. We recently…

Applications · Statistics 2016-05-26 Lukas Martig , Jürg Hüsler

Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two…

Methodology · Statistics 2018-05-01 Ayanendranath Basu , Abhijit Mandal , Nirian Martin , Leandro Pardo

We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow…

Data Analysis, Statistics and Probability · Physics 2013-06-25 Glen Cowan , Kyle Cranmer , Eilam Gross , Ofer Vitells

We propose a class of weighted $L_2$-type tests of fit to the Gamma distribution. Our novel procedure is based on a fixed point property of a new transformation connected to a Steinian characterization of the family of Gamma distributions.…

Methodology · Statistics 2020-02-25 Steffen Betsch , Bruno Ebner

A new test statistic based on success runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic $\chi^{2}$ test which ignores the…

Statistics Theory · Mathematics 2017-04-10 Frederik Beaujean , Allen Caldwell

The multivariate conditional probability distribution models the effects of a set of variables onto the statistical properties of another set of variables. In the study of systemic risk in a financial system, the multivariate conditional…

Risk Management · Quantitative Finance 2021-05-05 Tomaso Aste

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

This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method,…

Statistics Theory · Mathematics 2024-10-22 Mingxiang Cao , Yelong Qiu , Junyong Park