Accession Number : AD0661251

Title :   CONVERGENCE RATES FOR EMPIRICAL BAYES TWO-ACTION PROBLEMS II. CONTINUOUS CASE.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Johns,M. V. , Jr. ; Van Ryzin,J.

Report Date : 20 NOV 1967

Pagination or Media Count : 31

Abstract : A sequence of decision problems is considered where for each problem the observation has a probability density function of exponential type with parameter lambda where lambda is selected independently for each problem according to an unknown prior distribution G(lambda). It is supposed that in each of the problems, one of two possible actions (e.g., 'accept' or 'reject') must be taken. Under various assumptions, reasonably sharp upper bounds are found for the rate at which the risk of the nth problem approaches the smallest possible risk for certain refinements of the standard empirical Bayes procedures. For suitably chosen procedures, under situations likely to occur in practice, rates faster than n to the power (-1 + epsilon) may be obtained for arbitrarily small epsilon > 0. Arbitrarily slow rates can occur in pathological situations. (Author)

Descriptors :   (*DECISION THEORY, OPTIMIZATION), PROBABILITY DENSITY FUNCTIONS, EXPONENTIAL FUNCTIONS, MATHEMATICAL MODELS, CONVERGENCE, STATISTICAL ANALYSIS, THEOREMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE