Open Access
June 1998 Deconvolution density estimation on SO(N)
Peter T. Kim
Ann. Statist. 26(3): 1083-1102 (June 1998). DOI: 10.1214/aos/1024691089

Abstract

This paper develops nonparametric deconvolution density estimation over $SO(N)$, the group of $N \times N$ 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.

Citation

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Peter T. Kim. "Deconvolution density estimation on SO(N)." Ann. Statist. 26 (3) 1083 - 1102, June 1998. https://doi.org/10.1214/aos/1024691089

Information

Published: June 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0929.62042
MathSciNet: MR1635446
Digital Object Identifier: 10.1214/aos/1024691089

Subjects:
Primary: 62G05
Secondary: 58G25

Keywords: asymptotic bias , asymptotic variance , consistency , differentiable manifold , irreducible representations , unitary matrices

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 3 • June 1998
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