On the Independence of Quadratic Expressions

Abstract

Lety1,y2, · · ·*** be pairwise independent quadratic expressions inx, not necessarily homogeneous, wherexhas a multinormal distribution. Theny1,y2, …*** are alsomutuallyindependent. Various conditions for independence are given. In the Appendix, it is shown that x is a linear transformation of a vectorz, wherezhas a spherically symmetric distribution, and where they's depend on disjoint subsets of the components ofz.