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:

1968-10-01

Pagination or Media Count:

29.0

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