
Accession Number : AD0287478
Title : COMPLETE CLASS THEOREMS FOR UNBIASED ESTIMATION
Corporate Author : NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
Personal Author(s) : LASKA,EUGENE M.
Report Date : AUG 1962
Pagination or Media Count : 1
Abstract : Let fx, theta) be a given density function continuous in theta, theta epsilon omega, where omega is a compact subset of the real line. Let D be the class of randomized unbiased estimators, delta(x), of theta. For squared error loss function, the cls of Bayes soltions s shown to be essenly complete relative to D. If omega is convex then every purely randomized delta(x) is inadmissible since by the RaoBlackwell theorem epsilon delta (X)) has smaller risk. A theorem of STEIN CONCERNING LOCALLY BEST UNBIASED ESTIMATORS IS GENERALIZED TO PROVIDE CONDITIONS FOR UNIQUENES (and therefore adisibility) of Bayes solutions and functional equations for their determination. If the uniqueness condition is saisfied, then the bove lass is a complete class of admissible unbiased estimators. (Author)
Descriptors : *STATISTICAL DISTRIBUTIONS, *STATISTICAL FUNCTIONS, CONVEX SETS, DENSITY, EQUATIONS, INEQUALITIES, INTEGRALS, PROBABILITY
Distribution Statement : APPROVED FOR PUBLIC RELEASE