Deconvolution density estimation on \(\text{SO}(N)\). (English) Zbl 0929.62042

Kim, Peter T.

Ann. Stat. 26, No. 3, 1083-1102 (1998).

Summary: This paper develops nonparametric deconvolution density estimation over \(SL(N)\), 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.

MSC:

62G07	Density estimation
22C05	Compact groups
62G05	Nonparametric estimation
20G99	Linear algebraic groups and related topics

Keywords:

asymptotic variance; asymptotic bias; consistency; differentiable manifold; irreducible representations; unitary matrices

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