A Gaussian Compound Decision Bakeoff

A nonparametric mixture model approach to empirical Bayes compound decisions for the Gaussian location model is compared with a parametric empirical Bayes approach recently suggested by Martin and Walker and several recent more formal Bayes procedures. Martin and Walker (2013) have recently proposed a parametric empirical Bayes procedure for the classical Gaussian compound decision problem in which, Yi ∼ N (θi, 1), i = 1, 2, · · · , n and we wish to estimate θ ∈ R subject to squared error loss. I was curious to compare this procedure with the nonparametric empirical Bayes procedure recently introduced by Jiang and Zhang (2009) and further explored in Koenker and Mizera (2013). The latter approach is based on the nonparametric maximum likelihood estimator for mixture models of Kiefer and Wolfowitz (1956). The interior point computational approach suggested in Koenker and Mizera (2013) for the Kiefer-Wolfowitz MLE makes it feasible to study its performance much more easily.