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Location‐invariant Multi‐sample U ‐tests for Covariance Matrices with Large Dimension
Author(s) -
Ahmad M. Rauf
Publication year - 2017
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12262
Subject(s) - mathematics , statistics , covariance matrix , covariance , scatter matrix , estimator , multivariate statistics , invariant (physics) , dimension (graph theory) , estimation of covariance matrices , asymptotic distribution , multivariate normal distribution , statistical hypothesis testing , sample size determination , combinatorics , mathematical physics
For two or more multivariate distributions with common covariance matrix, test statistics for certain special structures of the common covariance matrix are presented when the dimension of the multivariate vectors may exceed the number of such vectors. The test statistics are constructed as functions of location‐invariant estimators defined as U ‐statistics, and the corresponding asymptotic theory is used to derive the limiting distributions of the proposed tests. The properties of the test statistics are established under mild and practical assumptions, and the same are numerically demonstrated using simulation results with small or moderate sample sizes and large dimensions.