# Accession Number:

## AD0287478

# Title:

## COMPLETE CLASS THEOREMS FOR UNBIASED ESTIMATION

# Descriptive Note:

# Corporate Author:

## NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES

# Personal Author(s):

# Report Date:

## 1962-08-01

# Pagination or Media Count:

## 1.0

# 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, deltax, 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 deltax 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