Fully Nonparametric Empirical Bayes Estimation via Projection Pursuit,

The fully nonparametric formulation of the empirical Bayes estimation problem considers m populations characterized by conditional sampling distributions chosen independently by some unspecified random mechanism. No parametric constraints are imposed on the family of possible sampling distributions or on the prior mechanism which selects them. The quantity to be estimated subject to squared-error loss for each population is defined by a functional TF where F is the population sampling cdf. The empirical Bayes estimator is based on n iid observations from each population where n 1. Asymptotically optimal procedures for this problem typically employ consistent nonparametric estimators of certain nonlinear conditional expectation functions. In this study a particular projection pursuit algorithm is used for this purpose. The proposed method is applied to the estimation of population means for several simulated data sets and one familiar real world data set. Certain possible extensions are discussed. Additional keywords nonparametric regression nonparametric estimation charts tablesdata. Author