The Annals of Statistics

Asymptotic Inference for Eigenvectors

David E. Tyler

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Abstract

Asymptotic procedures are given for testing certain hypotheses concerning eigenvectors and for constructing confidence regions for eigenvectors. These asymptotic procedures are derived under fairly general conditions on the estimates of the matrix whose eigenvectors are of interest. Applications of the general results to principal components analysis and canonical variate analysis are given.

Article information

Source
Ann. Statist. Volume 9, Number 4 (1981), 725-736.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176345514

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176345514

Mathematical Reviews number (MathSciNet)
MR619278

Zentralblatt MATH identifier
0474.62051

Subjects
Primary: 62H15: Hypothesis testing
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.) 62H25: Factor analysis and principal components; correspondence analysis 62E20: Asymptotic distribution theory

Keywords
Eigenvectors eigenprojections generalized inverses and asymptotic chi-square statistics principal components analysis canonical variate analysis elliptical distributions

Citation

Tyler, David E. Asymptotic Inference for Eigenvectors. Ann. Statist. 9 (1981), no. 4, 725--736. doi:10.1214/aos/1176345514. http://projecteuclid.org/euclid.aos/1176345514.


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