## The Annals of Statistics

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

### Asymptotic Inference for Eigenvectors

#### 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.