
Accession Number : AD0698501
Title : PARTIAL PRIOR INFORMATION: SOME EMPIRICAL BAYES AND GMINIMAX DECISION FUNCTIONS,
Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
Personal Author(s) : George,Stephen L.
Report Date : 30 OCT 1969
Pagination or Media Count : 178
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 nonBayes decision function for reasonably small N. When only knowledge of the class G is assumed, Gminimax 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 wellknown estimators by means of their Bayes risks and, in the empirical Bayes case, by means of their global risks for small N. (Author)
Descriptors : (*STATISTICAL ANALYSIS, *DECISION THEORY), DISTRIBUTION FUNCTIONS, MONTE CARLO METHOD, PROBABILITY, LINEAR PROGRAMMING, COMPUTER PROGRAMS, THESES
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE