ABSTRACT
This chapter discusses certain methods of obtaining Empirical Bayes (EB) point estimates are given, and they are applied to some of the standard distributions. Much of the writing on pure Bayes estimation is occupied with considerations of diffuse or non-informative prior distributions. The philosophical issue is reconciliation of the use of Bayes's theorem for inference, while not claiming sharp prior knowledge of parameter values. As usual however, calculation of Bayes and EB estimates, while straightforward, can be computationally difficult since multiple integration is required. The choice of a smoothing function remains open, but it should be influenced by knowledge of certain general characteristics of the Bayes estimator. Density estimation is an important topic in several branches of statistics and much further useful information will be found in B. W. Silverman. The chapter provides an outline of linear Bayes estimation and summarizes the method of calculating a linear Bayes estimator.
