Some Admissible Empirical Bayes Procedures

On Extended Admissible Procedures and their Nonstandard Bayes Risk

Semiparametrics, Nonparametrics and Empirical Bayes Procedures in Linear Models

In a classical parametric setup, a key factor in the implementation of the Empirical Bayes methodology is the incorporation of a suitable prior that is compatible with the parametric setup and yet lends to the estimation of the Bayes (shrinkage) factor in an empirical manner. The situation is more complex in semi-parametric and (ev,:,n more in) nonparametric models. Although the Dirichlet prior...

Empirical Bayes Estimation in Nonstationary Markov chains

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...

Empirical Bayes vs. Fully Bayes Variable Selection

For the problem of variable selection for the normal linear model, fixed penalty selection criteria such as AIC, Cp, BIC and RIC correspond to the posterior modes of a hierarchical Bayes model for various fixed hyperparameter settings. Adaptive selection criteria obtained by empirical Bayes estimation of the hyperparameters have been shown by George and Foster [2000. Calibration and Empirical B...

An Improved Bayes Empirical Bayes Estimator

Consider an experiment yielding an observable random quantity X whose distribution Fθ depends on a parameter θ with θ being distributed according to some distribution G0. We study the Bayesian estimation problem of θ under squared error loss function based on X, as well as some additional data available from other similar experiments according to an empirical Bayes structure. In a recent paper,...