A note on spiked Wishart matrices

Abstract

Consider the spiked complex Wishart matrices with sample size M and population size N. As N,M→∞ such that N/M→γ∈(0,1], Baik et al. (2005) established a phase transition of the largest eigenvalue. In this paper we show that some of their main results also hold true in the case where N/M→0. More precisely, we prove that limiting distribution of the largest eigenvalue is the finite GUE distribution.