Please use this identifier to cite or link to this item:
Title: Almost sure limit of the smallest eigenvalue of some sample correlation matrices
Authors: Xiao, H.
Zhou, W. 
Keywords: Random matrix
Sample correlation coefficient matrix
Sample covariance matrix
Smallest eigenvalue
Issue Date: Jan-2010
Citation: Xiao, H., Zhou, W. (2010-01). Almost sure limit of the smallest eigenvalue of some sample correlation matrices. Journal of Theoretical Probability 23 (1) : 1-20. ScholarBank@NUS Repository.
Abstract: Let X(n) = (Xij) be a p × n data matrix, where the n columns form a random sample of size n from a certain p-dimensional distribution. Let R(n) = (ρij) be the p × p sample correlation coefficient matrix of X(n), and S(n) = (1/n)X(n)(X(n))*-X̄X̄* be the sample covariance matrix of X(n), where X̄ is the mean vector of the n observations. Assuming that Xij are independent and identically distributed with finite fourth moment, we show that the smallest eigenvalue of R(n) converges almost surely to the limit (1-√c)2 as n → ∞ and p/n → c ∈ (0,∞). We accomplish this by showing that the smallest eigenvalue of S(n) converges almost surely to (1-√c)2. © Springer Science+Business Media, LLC 2009.
Source Title: Journal of Theoretical Probability
ISSN: 08949840
DOI: 10.1007/s10959-009-0270-2
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.


checked on Jul 14, 2018


checked on Jun 19, 2018

Page view(s)

checked on May 4, 2018

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.