
Accession Number : AD0679622
Title : UNIFORMLY MINIMUM VARIANCE UNBIASED ESTIMATORS WHEN THE PROBABILITY DISTRIBUTIONS HAVE A FINITE RANK.
Descriptive Note : Technical rept.,
Corporate Author : NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
Personal Author(s) : Takeuchi,Kei
Report Date : OCT 1968
Pagination or Media Count : 29
Abstract : The structure of the class of uniformly minimum variance unbiased estimators was discussed almost completely by R. R. Bahadur. Here we shall discuss the simple case when the class of probability distributions has only a finite number of linearly independent ones. Then it can be shown by elementary methods that an estimator is UMV if and only if it is measurable with respect to some finite field L. Necessary and sufficient conditions for a set A belong to L are obtained. The multinomial case is discussed. (Author)
Descriptors : (*ANALYSIS OF VARIANCE, *DECISION THEORY), DISTRIBUTION THEORY, MEASURE THEORY, STATISTICAL DISTRIBUTIONS, PROBABILITY, SET THEORY, THEOREMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE