UNIFORMLY MINIMUM VARIANCE UNBIASED ESTIMATORS WHEN THE PROBABILITY DISTRIBUTIONS HAVE A FINITE RANK.

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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

Author(s):
Takeuchi, Kei
Author Organization(s):
NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
Descriptive Note:
Technical rept.,
Pagination:
0029

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
IMM-372
Contract/Grant Number(s):
N00014-67-A-0467
Project Number(s):
NR-042-206
 Subject Terms
Communities of Interest:
No COI(s) Identified
Descriptor(s):
(*ANALYSIS OF VARIANCE, *DECISION THEORY), DISTRIBUTION THEORY, MEASURE THEORY, STATISTICAL DISTRIBUTIONS, PROBABILITY, SET THEORY, THEOREMS
Field(s)/Group(s):
Statistics and Probability
Keyword(s):
PROBABILITY DISTRIBUTIONS
Report Date:
1968 Oct 01