Schur^2-concavity properties of Gaussian measures, with applications to hypotheses testing
Probability
2017-01-17 v1 Statistics Theory
Statistics Theory
Abstract
The main results imply that the probability P(\ZZ\in A+\th) is Schur-concave/Schur-convex in (\th_1^2,\dots,\th_k^2) provided that the indicator 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 strict unless the set A is equivalent to a spherically symmetric set. Applications to testing hypotheses on multivariate means are given.
Keywords
Cite
@article{arxiv.1006.0502,
title = {Schur^2-concavity properties of Gaussian measures, with applications to hypotheses testing},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:1006.0502},
year = {2017}
}