Asymptotic optimality of multivariate linear hypothesis tests
type: Item
instance of: scholarly article
title: Asymptotic optimality of multivariate linear hypothesis tests
zbMATH Open document ID: 0636.62044
DOI: 10.1016/0047-259X(87)90159-X
author: Ludwig Baringhaus
published in: Journal of Multivariate Analysis
publication date: 1987-01-01T00:00:00Z
review text: The optimal exponential rate at which the Type II error probability of a multivariate linear hypothesis test can tend to zero while the Type I error probability is held fixed is given. The likelihood ratio test, the test of Hotelling and Lawley, the test of Bartlett, Nanda, and Pillai, and the test of Roy are shown to be asymptotically optimal in the sense that for each of these tests the exponential rate of convergence of the type II error probability attains the optimal value. Some other tests for the multivariate linear hypothesis are shown not to be asymptotically optimal.
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62F05
zbMATH DE Number: 4036936
zbMATH Keywords: limit of noncentrality parameters
zbMATH Keywords: fixed alternative
zbMATH Keywords: Pillai test
zbMATH Keywords: optimal exponential rate
zbMATH Keywords: Type II error probability
zbMATH Keywords: multivariate linear hypothesis test
zbMATH Keywords: likelihood ratio test
zbMATH Keywords: test of Hotelling and Lawley
zbMATH Keywords: test of Bartlett
zbMATH Keywords: test of Roy
zbMATH Keywords: exponential rate of convergence
MaRDI profile type: Publication
cites work: Q3255781
cites work: Q4107771
cites work: The Efficiency of Some Nonparametric Competitors of the $t$-Test
cites work: Exact Bahadur efficiencies for tests of the multivariate linear hypothesis
cites work: Bounds for the Power of Likelihood Ratio Tests and Their Asymptotic Properties
cites work: Q4079940
cites work: Q3219581
cites work: Distinctness of the eigenvalues of a quadratic form in a multivariate sample
cites work: METHODS OF STATISTICAL ANALYSIS APPROPRIATE FOR k SAMPLES OF TWO VARIABLES
cites work: Some New Test Criteria in Multivariate Analysis
description: scientific article; zbMATH DE number 4036936