Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero.
Chen, B. B.
Pan, G. M.
Date of Issue2012
School of Physical and Mathematical Sciences
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.
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