Upper Percentage Points of the Individual Roots of the Wishart Matrix

Abstract

Let S: pxp be distributed as central Wishart matrix with n degrees of freedom and let E(S) = n I sub p where I sub p is an identity matrix. Also, let theta (1)<...< theta (p) be the roots of S. In the report, the authors gave exact upper 10%, 5%, 2.5% and 1% points of the distributions of theta (i)(i=1,2, ..., p-1) for p=2(1)10 and n=(p+1) (1)20(2)30(5)50.