The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Common Principal Components in k Groups
Abstract
This article generalizes the method of principal components to so-called “common principal components” as follows: Consider the hypothesis that the covariance matrices Σ i for k populations are simultaneously diagonalizable. That is, there is an orthogonal matrix β such that β' Σ i β is diagonal for i = 1, …, k. I derive the normal-theory maximum likelihood estimates of the common component Σ i matrices and the log-likelihood-ratio statistics for testing this hypothesis. The solution has some favorable properties that do not depend on normality assumptions. Numerical examples illustrate the method. Applications to data reduction, multiple regression, and nonlinear discriminant analysis are sketched.
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Cites
THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS
FISHER, R. A. (1936) · Annals of Eugenics · doi:10.1111/j.1469-1809.1936.tb02137.x · Cited by 15,227
Linear Statistical Inference and its Applications: Second Editon
Rao, C. R. (1973) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316436 · Cited by 10,489
Multivariate Statistical Methods
(2008) · Encyclopedia of Public Health · doi:10.1007/978-1-4020-5614-7_2263 · Cited by 5,580
Linear Statistical Inference and Its Applications.
Robertson, C. A., & Rao, C. R. (1975) · Biometrics · doi:10.2307/2529568 · Cited by 3,598
Aspects of Multivariate Statistical Theory
Gleser, L. J. (1984) · Technometrics · doi:10.1080/00401706.1984.10487948 · Cited by 3,277
Aspects of multivariate statistical theory
Muirhead, R. J. 1. (1982) · Cited by 3,032
Aspects of Multivariate Statistical Theory
Muirhead, R. J. (1982) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316559 · Cited by 2,260
Multivariate Statistical Methods.
Clarke, G. M., & Morrison, D. F. (1977) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2344930 · Cited by 2,165
Between-Groups Comparison of Principal Components
Krzanowski, W. J. (1979) · Journal of the American Statistical Association · doi:10.1080/01621459.1979.10481674 · Cited by 533
Size and shape variation in the painted turtle. A principal component analysis.
JOLICOEUR, P., & Je, M. (1960) · PubMed · Cited by 423
Cited by
Bivariate line‐fitting methods for allometry
Warton, D. I., Wright, I. J., Falster, D. S., & Westoby, M. (2006) · Biological Reviews · doi:10.1017/s1464793106007007 · Cited by 2,319
Gaussian parsimonious clustering models
Celeux, G., & Govaert, G. (1995) · Pattern Recognition · doi:10.1016/0031-3203(94)00125-6 · Cited by 872
Measuring and comparing evolvability and constraint in multivariate characters
HANSEN, T. F., & HOULE, D. (2008) · Journal of Evolutionary Biology · doi:10.1111/j.1420-9101.2008.01573.x · Cited by 705
High-dimensional data clustering
Bouveyron, C., Girard, S., & Schmid, C. (2007) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2007.02.009 · Cited by 382
Metadata
- Authors
- Flury, B. N.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1984-12
- Volume
- 79
- Issue
- 388
- Pages
- 892-898
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2021576461
- Cited by
- 277
- References
- 12
- FWCI
- 3.49
- Type
- journal article
- Language
- en
- Open access
- closed
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