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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
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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References

Aitken, A. C. and Silverstone, H. (1942) On the estimation of statistical parameters. Proc. R. Soc. Edinburgh A 61, 186–194.Google Scholar
Barankin, E. (1949) Locally best unbiased estimators. Ann. Math. Statist. 20, 477–501.Google Scholar
Bartlett, M. S. (1933) Probability and chance in the theory of statistics. Proc. R. Soc. London A 141, 518–534.Google Scholar
Bartlett, M. S. (1936a) Statistical information and properties of sufficiency. Proc. R. Soc. London A 154, 124–137.Google Scholar
Bartlett, M. S.' (1936b) The information available in small samples. Proc. Camb. Phil. Soc. 36, 560–566.CrossRefGoogle Scholar
Bartlett, M. S. (1978) Introduction to Stochastic Processes , 3rd edn. Cambridge University Press.Google Scholar
Chapman, D. C. and Robbins, H. (1951) Minimum variance estimation without regularity assumptions. Ann. Math. Statist. 22, 581–586.CrossRefGoogle Scholar
Fisher, R. A. (1925) Theory of statistical estimation. Proc. Camb. Phil. Soc. 22, 700–725.CrossRefGoogle Scholar
Fisher, R. A. (1934) Two new properties of mathematical likelihood. Proc. R. Soc. London A 144, 285–307.Google Scholar
Hacking, I. (1965) Logic of Statistical Inference. Cambridge University Press.Google Scholar
Kiefer, J. (1952) On minimum variance estimates. Ann. Math. Statist. 23, 627–629.CrossRefGoogle Scholar
Moran, P. A. P. (1951) Estimation methods for evolutive processes. J. R. Statist. Soc. B 13, 141–146.Google Scholar
Pitman, E. J. G. (1979) Some Basic Theory for Statistical Inference. Chapman and Hall, London.Google Scholar
Ramsey, F. P. (1931) The Foundations of Mathematics, and Other Logical Essays. Routledge and Kegan Paul, London.Google Scholar