| Title:
|
Tests of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions (English) |
| Author:
|
Rublík, František |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
37 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
[61]-78 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Test statistics for testing some hypotheses on characteristic roots of covariance matrices are presented, their asymptotic distribution is derived and a confidence interval for the proportional sum of the characteristic roots is constructed. The resulting procedures are robust against violation of the normality assumptions in the sense that they asymptotically possess chosen significance level provided that the population characteristic roots are distinct and the covariance matrices of certain quadratic functions of the random vectors are regular. The null hypotheses considered include hypotheses on proportional sums of characteristic roots, hypotheses on equality of characteristic roots of covariance matrices of the underlying populations or on equality of their sums. (English) |
| Keyword:
|
violation of normality assumptions |
| MSC:
|
62E20 |
| MSC:
|
62F25 |
| MSC:
|
62F35 |
| MSC:
|
62H10 |
| MSC:
|
62H15 |
| idZBL:
|
Zbl 1263.62096 |
| idMR:
|
MR1825757 |
| . |
| Date available:
|
2009-09-24T19:37:10Z |
| Last updated:
|
2015-03-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135389 |
| . |
| Reference:
|
[1] Davis A. W.: Asymptotic theory for principal components analysis: non-normal case.Austral. J. Statist. 19 (1977), 206–212 MR 0501590, 10.1111/j.1467-842X.1977.tb01088.x |
| Reference:
|
[2] Kollo T., Neudecker H.: Asymptotics of eigenvalues and unit-length eigenvectors of sample variance and correlation matrices.J. Multivariate Anal. 47 (1993), 283–300 Zbl 0790.62055, MR 1247379, 10.1006/jmva.1993.1084 |
| Reference:
|
[3] Magnus J. R., Neudecker H.: Matrix Differential Calculus with Applications in Statistics and Econometrics.Wiley, New York 1988 Zbl 0912.15003, MR 0940471 |
| Reference:
|
[4] Mardia K. V., Kent J. T., Bibby J. M.: Multivariate Analysis.Academic Press, New York 1979 Zbl 0432.62029, MR 0560319 |
| Reference:
|
[5] Okamoto M.: Distinctness of the eigenvalues of a quadratic form in a multivariate sample.Ann. Statist. 1 (1973), 763–765 Zbl 0261.62043, MR 0331643, 10.1214/aos/1176342472 |
| Reference:
|
[6] Rao C. R., Mitra S. K.: Generalized Inverse of Matrices and its Applications.Wiley, New York 1971 Zbl 0261.62051, MR 0338013 |
| Reference:
|
[7] Rublík F.: On consistency of the MLE.Kybernetika 31 (1995), 45–64 MR 1324660 |
| Reference:
|
[8] Ruymgaart F. H., Yang S.: Some applications of Watson’s perturbation approach to random matrices.J. Multivariate Anal. 60 (1997), 48–60 Zbl 0927.62018, MR 1441458, 10.1006/jmva.1996.1640 |
| Reference:
|
[9] Schott J. R.: Some tests for common principal component subspaces in several groups.Biometrika 78 (1991), 771–777 Zbl 0850.62460, MR 1147013, 10.1093/biomet/78.4.771 |
| Reference:
|
[10] Schott J. R.: Asymptotics of eigenprojections of correlation matrices with some applications in principal components analysis.Biometrika 84 (1997), 327–337 Zbl 0883.62059, MR 1467050, 10.1093/biomet/84.2.327 |
| Reference:
|
[11] Tyler D. E.: The asymptotic distribution of principal component roots under local alternatives to multiple roots.Ann. Statist. 11 (1983), 1232–1242 Zbl 0546.62007, MR 0720268 |
| Reference:
|
[12] Waternaux C. M.: Asymptotic distribution of the sample roots for a nonnormal population.Biometrika 63 (1976), 639–645 Zbl 0352.62076, MR 0501582, 10.1093/biomet/63.3.639 |
| . |
