Density estimation on the Stiefel manifold

JOURNAL OF MULTIVARIATE ANALYSIS

卷:66

Article

Chikuse, Y

关键词: Stiefel manifold;    Grassmann manifold;    density estimation;    kernel density estimators;    asymptotic behavior of statistical measures;    decompositions of manifolds;    hypergeometric Functions with matrix argument;   

DOI  :  10.1006/jmva.1998.1747

来源: Elsevier

【 摘 要 】

This paper develops the theory of density estimation on the Stiefel manifold V-k,V-m where V-k,V-m is represented by the set of m x k matrices X such that X'X= I-k, the kxk identity 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 ibr small smoothing parameter matrix and/or for large sample size. Some decompositions of the Stiefel manifold V-k,V-m play 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. (C) 1998 Academic Press.

【 授权许可】

Free