This paper provides the Bayes estimators of the failure rate and reliability function for a one-parameter, exponential distribution by utilizing a point guess estimate of the parameter. For deriving the Bayes estimators, the prior distributions are chosen such that they are centered at the known prior values of parameters. The validity of proposed estimators is examined with respect to their ma...

Abstract. Empirical Bayes methods for Gaussian and binomial compound decision problems involving longitudinal data are considered. A new convex optimization formulation of the nonparametric (Kiefer-Wolfowitz) maximum likelihood estimator for mixture models is used to construct nonparametric Bayes rules for compound decisions. The methods are illustrated with some simulation examples as well as ...

Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein (2009), introduces a nonparametric maximum likelihood estimator of the mixture density subject to a monotonicity constraint on the resulting Bayes rule. The second, motivated by Ji...

The aim of the present paper is to obtain Bayes estimators for the oospring mean of a simple branching process with a power series oospring probability distribution. We study the sensitivity behavior of the obtained estimators with respect to the choice of the loss function. We propose a minimax criterion using the Bayes risk for ranking the eeectiveness (in the sense of robustness) of the loss...

In this study, the maximum likelihood estimation (MLE) and Bayes estimation are exploited to make interval estimation based on adaptive progressive TypeII censoring for the Burr Type-XII distribution. Explicit form for the parameters of Bayes estimator doesn’t exist, so, Markov Chain Monte Carlo (MCMC) method is used as approximation to find posterior mean under squared error loss function. Rea...

An important aspect of mixture modeling concerns the selection of the number of mixture components. In this paper, we discuss the Bayes factor as a selection tool. The discussion will focus on two aspects: (i) computation of the Bayes factor and (ii) prior sensitivity. For the computation, we propose a variant of Chib’s estimator that accounts for the non-identifiability of the mixture componen...

The use of a linear estimator to estimate random eeects in a Mixed Model is not necessarily optimal if the prior distribution is non-normal. Either a frequentist or Bayesian approach leads to the Best Linear Unbiased Predictor (BLUP), but an empirical Bayes approach produces a multivariate, non-linear, single-pass kernel-based estimator (the General Empirical Bayes or GEB es-timator) that allow...