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

Iosif Pinelis

Journal of Multivariate Analysis, 2014, vol. 124, issue C, 384-397

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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2013.11.011

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