Schur2-concavity properties of Gaussian measures, with applications to hypotheses testing
Abstract
The main results imply that the probability P(∈ A+) is Schur-concave/Schur-convex in (12,…,k2) provided that the indicator function of a set A in k is so, respectively; here, =(1,…,k) in k and is a standard normal random vector in 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.
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