Schur < sup> 2 -concavity properties of Gaussian measures, with applications to hypotheses testing

Document Type

Article

Publication Date

2-1-2014

Abstract

The main results imply that the probability P(Z∈ A+ θ) is Schur-concave/Schur-convex in (θ12,...,θk2) provided that the indicator function of a set A in Rk is so, respectively; here, θ=(θ1,...,θk)∈Rk and Z is a standard normal random vector in Rk. 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. © 2013 Elsevier Inc.

Publication Title

Journal of Multivariate Analysis

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