Deconvolution Density Estimation on SO(N)

This paper develops nonparametric deconvolution density estimation over SO(N), the group of N N orthogonal matrices of determinant one. 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 speciic rates of convergence achieved under suucient smoothness conditions. Application to empirical Bayes prior estimation and inference is also discussed.