From Shape-Constrained Density Estimation to Empirical Bayes Decision Rules
by Ivan Mizera
Abstract: A shape constrained maximum likelihood variant of the kernel based empirical Bayes rule proposed by Brown and Greenshtein (2009) for the classical Gaussian compound decision problem is described and some simulation comparisons are presented. The simulation evidence suggests that the shape constrained Bayes rule improves substantially on the performance of the unconstrained kernel estimate for the Bayes rule. Two variants of the generalized non-parametric maximum likelihood (Kiefer-Wolfowitz) Bayes rule recently proposed by Jiang and Zhang (2009) are also studied, from the similar viewpoint of mathematical convex optimization and modern interior point methods; the latter, regarding the computation of the Kiefer-Wolfowitz estimator, substantially improve upon the prevailing EM approach.
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