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A Local Parameterization of Orthogonal and Semi-Orthogonal Matrices with Applications

  • Boik, Robert J.
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    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.

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

    Volume (Year): 67 (1998)
    Issue (Month): 2 (November)
    Pages: 244-276

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    Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:244-276
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    1. 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.
    2. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
    3. James Steiger & Michael Browne, 1984. "The comparison of interdependent correlations between optimal linear composites," Psychometrika, Springer, vol. 49(1), pages 11-24, March.
    4. Ledyard Tucker, 1958. "An inter-battery method of factor analysis," Psychometrika, Springer, vol. 23(2), pages 111-136, June.
    5. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
    6. 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.
    7. Douglas Clarkson & Robert Jennrich, 1988. "Quartic rotation criteria and algorithms," Psychometrika, Springer, vol. 53(2), pages 251-259, June.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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