Schur2-concavity properties of Gaussian measures, with applications to hypotheses testing
Document Type
Article
Publication Date
2-2014
Department
Department of Mathematical Sciences
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.
Publication Title
Journal of Multivariate Analysis
Recommended Citation
Pinelis, I.
(2014).
Schur2-concavity properties of Gaussian measures, with applications to hypotheses testing.
Journal of Multivariate Analysis,
124, 384-397.
http://doi.org/10.1016/j.jmva.2013.11.011
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/6773
