PARTIAL PRIOR INFORMATION: SOME EMPIRICAL BAYES AND G-MINIMAX DECISION FUNCTIONS,
Abstract
If the prior probability distribution function G of the parameters in a statistical decision theory model is not completely specified then a Bayes decision function cannot be obtained. However, in many cases there may be some partial (i.e., incomplete) prior information concerning G. The types of partial prior information considered in this paper is of two kinds: (1) N past observations on the compound distribution f sub G(t) or (2) knowledge of a restrictive class G to which the unknown G is assumed to belong. When past observations are available, empirical Bayes decision functions are found which are: (1) asymptotically optimal (2) easy to apply and (3) better than some optimal non-Bayes decision function for reasonably small N. When only knowledge of the class G is assumed, G-minimax decision functions are found. In all cases, estimators for the parameters of the normal and Bernoulli processes are found using a quadratic loss function. These estimators are then compared to each other and to other well-known estimators by means of their Bayes risks and, in the empirical Bayes case, by means of their global risks for small N. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 30, 1969
- Accession Number
- AD0698501
Entities
People
- Stephen L. George
Organizations
- Southern Methodist University