UNIFORMLY MINIMUM VARIANCE UNBIASED ESTIMATORS WHEN THE PROBABILITY DISTRIBUTIONS HAVE A FINITE RANK.
NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
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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
- Statistics and Probability