Classical approaches to estimating the rate of occurrence of events perform poorly when data are few. Maximum Likelihood Estimators result in overly optimistic point estimates of zero for situations where there have been no events. Alternative empirical based approaches have been proposed based on median estimators or noninformative prior distributions. While these alternatives offer an improve...

Classical approaches to estimating the rate of occurrence of events perform poorly when data are few. Maximum Likelihood Estimators result in overly optimistic point estimates of zero for situations where there have been no events. Alternative empirical based approaches have been proposed based on median estimators or noninformative prior distributions. While these alternatives offer an improve...

Abstract. This paper clarifies the generalization errors of Bayes and Gibbs estimations in non-identifiable statistical models based on algebraic geometry and empirical process theory. First, the concrete results are proven for statistical models with normal crossing singularities. Second, they are generalized for all models by using Hironaka’s desingularization theorem. The Bayes generalizatio...

Abstract. Empirical Bayes methods for Gaussian and binomial compound decision problems involving longitudinal data are considered. A recent convex optimization reformulation of the nonparametric maximum likelihood estimator of Kiefer and Wolfowitz (1956) is employed to construct nonparametric Bayes rules for compound decisions. The methods are illustrated with an application to predicting baseb...

This paper deals with a monotone empirical Bayes test δ∗ n for a truncation parameter distribution using the linex loss. The asymptotic optimality of δ∗ n is investigated. Under very mild conditions, it is shown that δ∗ n is asymptotically optimal with a rate of order n. This rate improves the empirical Bayes test δ n of Xu and Shi (2004) in the sense that faster convergence rate is achieved un...

Consider the gene ranking problem of replicated microarray time course experiments where there are multiple biological conditions, and genes of interest are those whose temporal profiles are different across conditions. We derive the multi-sample multivariate empirical Bayes statistic for ranking genes in the order of differential expression, from both longitudinal and cross-sectional replicate...

We investigate the empirical Bayes estimation problem of multivariate regression coefficients under squared error loss function. In particular, we consider the regression model Y = Xβ+ ε, where Y is an m-vector of observations, X is a known m× k matrix, β is an unknown k-vector, and ε is anm-vector of unobservable random variables. The problem is squared error loss estimation of β based on some...

Empirical Bayes modeling has a long and celebrated history in statistical theory and applications. After a brief review of the literature, we propose a new dynamic empirical Bayes modeling approach which provides flexible and computationally efficient methods for the analysis and prediction of longitudinal data from many individuals. This dynamic empirical Bayes approach pools the cross-section...