Deconvolution density estimation on SO(N)

• 成果类型: Article
• 署名作者: Kim, PT
• 署名单位: University of Guelph; Yonsei University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1024691089
• 发表日期: 1998
• 页码: 1083-1102
• 关键词: spherical regression; orientation statistics; nonparametric deconvolution; DIRECTIONAL-DATA; variables; errors

摘要

This paper develops nonparametric deconvolution density estimation over SO(N), the group of N x N orthogonal matrices of determinant 1. The methodology is to use the group and manifold structures to adapt the Euclidean deconvolution techniques to this Lie group environment. This is achieved by employing the theory of group representations explicit to SO(N). General consistency results are obtained with specific rates of convergence achieved under sufficient smoothness conditions. Application to empirical Bayes prior estimation and inference is also discussed.