Empirical Bayes Estimation for Exponential Model Using Non-parameter Polynomial Density Estimator

Abstract

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 the parameter of the exponential distribution under squared error and LINEX loss functions. We use numerical examples to compare the empirical Bayes estimators we obtained under squared error and LINEX loss functions and we get the result of the mean square error of the empirical Bayes estimator under LINEX loss is usually smaller than the estimator under squared error loss function, so it is more better.