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

Robert J. Boik

Journal of Multivariate Analysis, 2005, vol. 96, issue 1, 136-171

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.

Keywords: Confidence; interval; Correlation; matrix; Covariance; matrix; Edgeworth; expansion; Eigenvalue; Principal; components; analysis; Saddlepoint; approximation (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (2)

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