Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero
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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Online Access: | https://hdl.handle.net/10356/98864 http://hdl.handle.net/10220/12678 |