# Schur^2-concavity properties of Gaussian measures, with applications to hypotheses testing - Mathematics > Probability

Schur^2-concavity properties of Gaussian measures, with applications to hypotheses testing - Mathematics > Probability - Download this document for free, or read online. Document in PDF available to download.

Abstract: The main results imply that the probability P\ZZ\in A+\th isSchur-concave-Schur-convex in \th 1^2,\dots,\th k^2 provided that theindicator function of a set A in \R^k is so, respectively; here,\th=\th 1,\dots,\th k in \R^k and \ZZ is a standard normal random vector in\R^k. Moreover, it is shown that the Schur-concavity-Schur-convexity is strictunless the set A is equivalent to a spherically symmetric set. Applications totesting hypotheses on multivariate means are given.

Author: ** Iosif Pinelis**

Source: https://arxiv.org/