A Local Parameterization of Orthogonal and Semi-Orthogonal Matrices with Applications
This article describes a local parameterization of orthogonal and semi-orthogonal matrices. The parameterization leads to a unified approach for obtaining the asymptotic joint distributions of estimators of singular-values and -vectors, and of eigen-values and -vectors. The singular- or eigen-values can have arbitrary multiplicities. The approach is illustrated on principal components analyzes, canonical correlation analysis, inter-battery factory analysis, and reduced-rank regression.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 67 (1998)
Issue (Month): 2 (November)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
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.:
- Fujikoshi, Yasunori, 1974. "The likelihood ratio tests for the dimensionality of regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 4(3), pages 327-340, September.
- Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
- Ledyard Tucker, 1958. "An inter-battery method of factor analysis," Psychometrika, Springer, vol. 23(2), pages 111-136, June.
- James Steiger & Michael Browne, 1984. "The comparison of interdependent correlations between optimal linear composites," Psychometrika, Springer, vol. 49(1), pages 11-24, March.
- Fang, C. & Krishnaiah, P. R., 1982. "Asymptotic distributions of functions of the eigenvalues of some random matrices for nonnormal populations," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 39-63, March.
- Seo, T. & Kanda, T. & Fujikoshi, Y., 1995. "The Effects of Nonnormality of Tests for Dimensionality in Canonical Correlation and MANOVA Models," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 325-337, February.
- Douglas Clarkson & Robert Jennrich, 1988. "Quartic rotation criteria and algorithms," Psychometrika, Springer, vol. 53(2), pages 251-259, June.
- Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
- Kollo, T. & Neudecker, H., 1993. "Asymptotics of Eigenvalues and Unit-Length Eigenvectors of Sample Variance and Correlation Matrices," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 283-300, November.
- Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
- Eaton, M. L. & Tyler, D., 1994. "The Asymptotic Distribution of Singular-Values with Applications to Canonical Correlations and Correspondence Analysis," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 238-264, August.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:244-276. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.