Density Estimation on the Stiefel Manifold
AbstractThis paper develops the theory of density estimation on the Stiefel manifoldVk,Â m, whereVk,Â mis represented by the set ofm-kmatricesXsuch thatX'X=Ik, thek-kidentity matrix. The density estimation by the method of kernels is considered, proposing two classes of kernel density estimators with small smoothing parameter matrices and for kernel functions of matrix argument. Asymptotic behavior of various statistical measures of the kernel density estimators is investigated for small smoothing parameter matrix and/or for large sample size. Some decompositions of the Stiefel manifoldVk,Â mplay useful roles in the investigation, and the general discussion is applied and examined for a special kernel function. Alternative methods of density estimation are suggested, using decompositions ofVk,Â m.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 66 (1998)
Issue (Month): 2 (August)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Chikuse, Yasuko, 1991. "Asymptotic expansions for distributions of the large sample matrix resultant and related statistics on the Stiefel manifold," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 270-283, November.
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- Constantine, A. G. & Muirhead, R. J., 1976. "Asymptotic expansions for distributions of latent roots in multivariate analysis," Journal of Multivariate Analysis, Elsevier, vol. 6(3), pages 369-391, September.
- Chikuse, Yasuko, 1990. "Distributions of orientations on Stiefel manifolds," Journal of Multivariate Analysis, Elsevier, vol. 33(2), pages 247-264, May.
- Chikuse, Yasuko, 2003. "Concentrated matrix Langevin distributions," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 375-394, May.
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