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Title: | Almost sure limit of the smallest eigenvalue of sample correlation matrix | Authors: | XIAO HAN | Keywords: | sample covariance matrix, sample correlation matrix, smallest eigenvalue, random matrix, spectral distribution, Marcenko-Pastur law | Issue Date: | 29-Nov-2006 | Citation: | XIAO HAN (2006-11-29). Almost sure limit of the smallest eigenvalue of sample correlation matrix. ScholarBank@NUS Repository. | Abstract: | Suppose we have a data matrix consisting of independent and identically distributed entries with finite fourth moment, we show that the smallest eigenvalue of the sample correlation matrix converges almost surely to a constant provided that the ration of dimensions of the data matrix goes to a positive constant. We accomplish this by establishing a similar result for the sample covariance matrix. The proof relies strongly on existing results about the simplified sample covariance matrix. | URI: | http://scholarbank.nus.edu.sg/handle/10635/15593 |
Appears in Collections: | Master's Theses (Open) |
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