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 Rao-Blackwell 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