Second-order accurate inference on eigenvalues of covariance and correlation matrices

Authors:
Robert J. Boik
Affiliations:
Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717-2400, USA
Venue:
Journal of Multivariate Analysis
Year:
2005

Citing 2
Cited 2

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Model-based principal components of correlation matrices

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Abstract

Edgeworth expansions and saddlepoint approximations for the distributions of estimators of certain eigenfunctions of covariance and correlation matrices are developed. These expansions depend on second-, third-, and fourth-order moments of the sample covariance matrix. Expressions for and estimators of these moments are obtained. The expansions and moment expressions are used to construct second-order accurate confidence intervals for the eigenfunctions. The expansions are illustrated and the results of a small simulation study that evaluates the finite-sample performance of the confidence intervals are reported.