Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero

• Main Authors: Chen, B. B., Pan, G. M.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Online Access: https://hdl.handle.net/10356/98864; http://hdl.handle.net/10220/12678
• Institution: Nanyang Technological University

Let Xp = (s1, . . . , sn) = (Xij )p×n where Xij ’s are independent and identically distributed (i.i.d.) random variables with EX11 = 0, EX2 11 = 1 and EX4 11 <1. It is showed that the largest eigen- value of the random matrix Ap = 1 2√np (XpX′p −nIp) tends to 1 almost surely as p→∞,n→∞ with p/n→0...