Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/98864
Title: Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero
Authors: Chen, B. B.
Pan, G. M.
Issue Date: 2012
Source: Chen, B. B., & Pan, G. M. (2012). Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero. Bernoulli, 18(4), 1405-1420.
Series/Report no.: Bernoulli
Abstract: 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.
URI: https://hdl.handle.net/10356/98864
http://hdl.handle.net/10220/12678
ISSN: 1350-7265
DOI: http://dx.doi.org/10.3150/11-BEJ381
Rights: © 2012 ISI/BS. This paper was published in Bernoulli and is made available as an electronic reprint (preprint) with permission of Bernoulli Society for Mathematical Statistics and Probability. The paper can be found at the following official DOI: [http://dx.doi.org/10.3150/11-BEJ381]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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