In Bayesian hierarchical modeling, it is often appealing to allow the conditional density of an (observable or unobservable) random variable Y to change flexibly with categorical and continuous predictors X. A mixture of regression models is proposed, with the mixture distribution varying with X. Treating the smoothing parameters and number of mixture components as unknown, the MLE does not exi...

The paper proposes empirical Bayes (EB) estimators for simultaneous estimation of means in the natural exponential family (NEF) with quadratic variance functions (QVF) models. Morris (1982, 1983a) characterized the NEF-QVF distributions which include among others the binomial, Poisson and normal distributions. In addition to the EB estimators, we provide approximations to the MSE’s of t...

In this study, we study the empirical Bayes estimation of the parameter of the exponential distribution. In the empirical Bayes procedure, we employ the non-parameter polynomial density estimator to the estimation of the unknown marginal probability density function, instead of estimating the unknown prior probability density function of the parameter. Empirical Bayes estimators are derived for...

Abstract When the dimension of data is comparable to or larger than number samples, principal components analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an empirical Bayes PCA method that reduces noise by estimating a joint prior distribution for components. EB-PCA based on classical Kiefer–Wolfowitz non-parametric maximum likelihood estimator estimation,...

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 w...