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The ‘ideal’ estimation equation

Published online by Cambridge University Press:  14 July 2016

M. S. Bartlett
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Abstract

The Cramér–Rao inequality for the variance of an unbiassed estimator is first recalled, and the value of the ‘ideal' equation of estimation existing if the minimum bound is reached illustrated by examples. When this estimation equation is not available, the more general inequality due to Kiefer is more relevant. The analogous estimation equation corresponding to the attaining of the more general minimum bound is again illustrated by examples; and the general theory, which is also available for more than one parameter, is indicated for any location and/or scaling problem.

Keywords

UNBIASSED ESTIMATORMINIMUM BOUNDESTIMATION EQUATION

Information

Type
Part 5 — Statistical Theory
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982, pp. 187 - 200
Copyright
Copyright © 1982 Applied Probability Trust 

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