A better approximation of moments of the eigenvalues and eigenvectors of the sample covariance matrix. (English) Zbl 1325.62118
Summary: D. N. Lawley [Biometrika 43, 128–136 (1956; Zbl 0070.37603)] obtained an approximation, through the first terms of a series expansion, of certain moments of an eigenvalue of the sample covariance matrix. The aim of this paper is to improve that approximation and to calculate a similar approximation for certain moments of the associated eigenvector. The results have practical applications in certain fields of Statistics, such as Influence Analysis.
MSC:
| 62H25 | Factor analysis and principal components; correspondence analysis |
| 62F12 | Asymptotic properties of parametric estimators |
Keywords:
eigenvalues; eigenvectors; sample covariance matrix; principal component analysis; influence analysisCitations:
Zbl 0070.37603References:
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| [4] | Lawley, D. N., Test of significance for the latent roots of covariance and correlation matrices, Biometrika, 43, 128-136 (1956) · Zbl 0070.37603 |
| [5] | Muñoz Pichardo, J. M.; Muñoz García, J.; Moreno Rebollo, J. L.; Pino Mejías, R., A new approach to influence analysis in linear models, Sankhyā Ser. A, 57, 393-409 (1995) · Zbl 0857.62071 |
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