On the non-stochastic ordering of some quadratic forms

Éric Marchand and William E. Strawderman

Statistics & Probability Letters, 2020, vol. 163, issue C

Abstract: For Y=‖aZ+θ‖2, a>0, Z∼Np(θ,Ip), θ≠{0}, we show that the distribution of Y is not stochastically ordered in a>0. We provide extensions to spherically symmetric, elliptically symmetric, and skew-normal distributions, as well as to other quadratic forms.

Keywords: Elliptical symmetric; Normal distribution; Quadratic forms; Skew-normal; Spherically symmetric; Stochastic ordering (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108799

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