On the non-stochastic ordering of some quadratic forms

摘要

For Y = parallel to aZ + theta parallel to(2), a > 0, Z similar to N-p(theta, I-p), theta not equal {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. (C) 2020 Elsevier B.V. All rights reserved.