Comments on a result of Yin, Bai, and Krishnaiah for large dimensional multivariate F matrices

Abstract

A theorem in Yin, Bai, and Krishnaiah ( J. Multivariate Anal. 13 (1983), 508–516) shows that the smallest eigenvalue of a class of large dimensional sample covariance matrices stays almost surely bounded away from zero. The theorem assumes a certain restriction on the class of matrices. With slight modifications of the proof in op cit, it is shown here that the theorem is true for all relevant matrices.