Title

Eigenprojections And The Equality Of Latent Roots Of A Correlation Matrix

Authors

Authors

J. R. Schott

Comments

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Abbreviated Journal Title

Comput. Stat. Data Anal.

Keywords

chi-squared test; principal components analysis; Computer Science, Interdisciplinary Applications; Statistics &; Probability

Abstract

In this paper, we consider the inference problem regarding the equality of the q smallest latent roots of a correlation matrix. A statistic, which is a function of the eigenprojection associated with the q smallest latent roots of the sample correlation matrix, is shown to have an asymptotic normal distribution. The expected value of this statistic is the zero vector if, and only if, the q smallest latent roots of the population correlation matrix are equal. This permits the construction of a chi-squared test statistic for the test of the equality of the q smallest latent roots of a population correlation matrix. Simulation results indicate that this test is superior to others currently in use in terms of achieving the nominal significance level for small sample sizes.

Journal Title

Computational Statistics & Data Analysis

Volume

23

Issue/Number

2

Publication Date

1-1-1996

Document Type

Article

Language

English

First Page

229

Last Page

238

WOS Identifier

WOS:A1996VZ70000003

ISSN

0167-9473

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