Deconvolution density estimation on SO(N)

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.