Eigenprojections And The Equality Of Latent Roots Of A Correlation Matrix

    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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