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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:96

Article

Boik, RJ

关键词: confidence interval;    correlation matrix;    covariance matrix;    edgeworth expansion;    eigenvalue;    principal components analysis;    saddlepoint approximation;   

DOI  :  10.1016/j.jmva.2004.09.009

来源: Elsevier

【 摘 要 】

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. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free