A note on spiked Wishart matrices

Dang-Zheng Liu and Yanhui Wang

Statistics & Probability Letters, 2017, vol. 127, issue C, 1-6

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.

Keywords: BBP phase transition; GUE; Largest eigenvalue; Sample covariance matrices (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.03.019

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