Schur2-concavity properties of Gaussian measures, with applications to hypotheses testing

JOURNAL OF MULTIVARIATE ANALYSIS

卷:124

Article

Pinelis, Iosif

关键词: Probability inequalities;    Geometric probability;    Gaussian measures;    Multivariate normal distribution;    Mixtures;    Majorization;    Stochastic ordering;    Schur convexity;    Hypothesis testing;    Asymptotic properties of tests;    Asymptotic relative efficiency;    p-mean tests;    Multivariate means;    Reflection groups;   

DOI  :  10.1016/j.jmva.2013.11.011

来源: Elsevier

【 摘 要 】

The main results imply that the probability P(Z is an element of A + theta) is Schur-concave/Schur-convex in (theta(2)(1),...,theta(2)(k)) provided that the indicator function of a set A in R-k is so, respectively; here, theta = (theta(1),...,theta(k)) is an element of R-k and Z is a standard normal random vector in R-k. Moreover, it is shown that the Schur-concavity/Schur-convexity is strict unless the set A is equivalent to a spherically symmetric set. Applications to testing hypotheses on multivariate means are given. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free