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

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  • Pinelis, Iosif

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.

Suggested Citation

  • Pinelis, Iosif, 2014. "Schur2-concavity properties of Gaussian measures, with applications to hypotheses testing," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 384-397.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:384-397
    DOI: 10.1016/j.jmva.2013.11.011
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    References listed on IDEAS

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    1. Strawderman, William E., 1974. "Minimax estimation of location parameters for certain spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 4(3), pages 255-264, September.
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    Cited by:

    1. Anders Bredahl Kock & David Preinerstorfer, 2019. "Power in High‐Dimensional Testing Problems," Econometrica, Econometric Society, vol. 87(3), pages 1055-1069, May.

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