Expectation of Elementary Symmetric Functions of a Wishart Matrix

Abstract

Some conjectures made by De Waal [Ann. Math. Statist. 43 (1972) 344-347] on the expectation of elementary symmetric functions of the roots of a noncentral Wishart matrix are proved true. The method of proof is through a simple, though perhaps obscure, property of these elementary symmetric functions and simple properties of the Wishart distribution.