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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.
Appears in Collections:Master's Theses (Open)

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