NDLI: On the Asymptotic Behavior of the Sample Estimates of Eigenvalues and Eigenvectors of Covariance Matrices

Content Provider	IEEE Xplore Digital Library
Author	Mestre, X.
Copyright Year	1991
Abstract	This paper analyzes the asymptotic behavior of the sample estimators of the eigenvalues and eigenvectors of covariance matrices. Rather than considering traditional large sample-size asymptotics, in this paper the focus is on limited sample size situations, whereby the number of available observations is comparable in magnitude to the observation dimension. Using tools from random matrix theory, the asymptotic behavior of the traditional sample estimates is investigated under the assumption that both the sample size and the observation dimension tend to infinity, while their quotient converges to a positive quantity. Assuming that an asymptotic eigenvalue splitting condition is fulfilled, closed form asymptotic expressions of these estimators are derived, proving inconsistency of the traditional sample estimators in these asymptotic conditions. The derived expressions are shown to provide a valuable insight into the behavior of the sample estimators in the small sample size regime.
Sponsorship	IEEE Signal Processing Society
Starting Page	5353
Ending Page	5368
Page Count	16
File Size	939740
File Format	PDF
ISSN	1053587X
Volume Number	56
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-11-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Eigenvalues and eigenfunctions Covariance matrix Signal processing Maximum likelihood estimation H infinity control Econometrics Direction of arrival estimation Array signal processing Frequency estimation Gaussian processes sample eigenvectors Random matrix theory sample covariance matrix sample eigenvalues Random Matrix Theory
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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