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Asymptotic distributions of functions of the eigenvalues of some random matrices for nonnormal populations

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Author Info
Fang, C.
Krishnaiah, P. R.
Abstract

The authors investigated the asymptotic joint distributions of certain functions of the eigenvalues of the sample covariance matrix, correlation matrix, and canonical correlation matrix in nonnull situations when the population eigenvalues have multiplicities. These results are derived without assuming that the underlying distribution is multivariate normal. In obtaining these expressions, Edgeworth type expansions were used.

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Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 12 (1982)
Issue (Month): 1 (March)
Pages: 39-63
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Handle: RePEc:eee:jmvana:v:12:y:1982:i:1:p:39-63

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Keywords: Nonnormal distributions Edgeworth type expansion asymptotic distribution theory principal component analysis canonical correlation analysis;

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Masanobu Taniguchi & Madan Puri, 1995. "Higher order asymptotic theory for normalizing transformations of maximum likelihood estimators," Annals of the Institute of Statistical Mathematics, Springer, vol. 47(3), pages 581-600, September. [Downloadable!] (restricted)
  2. Haruhiko Ogasawara, 2009. "Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(4), pages 995-1017, December. [Downloadable!] (restricted)
  3. P. Bentler, 1983. "Some contributions to efficient statistics in structural models: Specification and estimation of moment structures," Psychometrika, Springer, vol. 48(4), pages 493-517, December. [Downloadable!] (restricted)
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