Density Estimation on the Stiefel Manifold

✍ Scribed by Yasuko Chikuse

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 285 KB
• Volume: 66
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1998.1747

✦ Synopsis

This paper develops the theory of density estimation on the Stiefel manifold V k, m , where V k, m is represented by the set of m_k matrices X such that X$X=I k , the k_k 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 for small smoothing parameter matrix andÂor for large sample size. Some decompositions of the Stiefel manifold V k, 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 of V k, m .