Expectations of products of quadratic forms in normal variables

Abstract

Let x be normally distributed N _p (μ∑) where ∑is positive definite and define the quadratic form and product of quadratic forms. We present explicite simple expressions for the raw moments and cumulants, of arbitrary order, of a quadratic form Q(x) in normal variates on R ^pand of the expectation of a product Q _kof an arbitrary number of quadratic forms in normally distributed variables