Abstract
Deconvolution is an important class of inverse problems. The goal of this paper is to develop the optimality properties of deconvolution density estimators on the noncommutative and noncompact six-dimensional Euclidean motion group. The idea is that if the underlying random object is a composition of several independent objects, then the underlying density is a convolution of densities of those independent objects. Therefore, deconvolution allows one to recover the main components of the mixture. We illustrate this with some numerical work.
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