The Annals of Statistics

On Wielandt's Inequality and Its Application to the Asymptotic Distribution of the Eigenvalues of a Random Symmetric Matrix

Morris L. Eaton and David E. Tyler

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Abstract

A relatively obscure eigenvalue due to Wielandt is used to give a simple derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix. The asymptotic distributions are obtained under a fairly general setting. An application of the general theory to the bootstrap distribution of the eigenvalues of the sample covariance matrix is given.

Article information

Source
Ann. Statist. Volume 19, Number 1 (1991), 260-271.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176347980

Digital Object Identifier
doi:10.1214/aos/1176347980

Mathematical Reviews number (MathSciNet)
MR1091849

Zentralblatt MATH identifier
0742.62015

JSTOR
links.jstor.org

Subjects
Primary: 62H25: Factor analysis and principal components; correspondence analysis
Secondary: 62E20: Asymptotic distribution theory

Keywords
Bootstrap covariance matrix eigenvalues random symmetric matrices

Citation

Eaton, Morris L.; Tyler, David E. On Wielandt's Inequality and Its Application to the Asymptotic Distribution of the Eigenvalues of a Random Symmetric Matrix. Ann. Statist. 19 (1991), no. 1, 260--271. doi:10.1214/aos/1176347980. http://projecteuclid.org/euclid.aos/1176347980.


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