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

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.

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Year of publication:	2014
Authors:	Pinelis, Iosif
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 124.2014, C, p. 384-397
Publisher:	Elsevier
Subject:	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

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011041960