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VI.—Unbiased Statistics with Minimum Variance

Published online by Cambridge University Press:  14 February 2012

A. Bhattacharyya
A. Bhattacharyya
Affiliation:
Statistical Laboratory, Calcutta.
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Synopsis

The problem considered is that of the estimation of a statistical parameter from a sample of values of the variate or variates concerned. Reference is made to the method of unbiased statistics with minimum variance, developed by Aitken and Silverstone. The principal result obtained by these authors is generalized, and an inequality involving the variances of unbiased statistics is obtained. Several examples illustrating the theory are appended.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 63 , Issue 1 , 1950 , pp. 69 - 77
Copyright
Copyright © Royal Society of Edinburgh 1950

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References

References to Literature

Aitken, A. C., and Silverstone, H., 1941-1942. “On the Estimation of Statistical Parameters”, Proc. Roy. Soc. Edin., A, LXI, 186–194.Google Scholar
Bhattacharyya, A., 1946. “On some Analogues of the Amount of Information and their Uses in Statistical Estimation”, Sankhya, VIII, 1–14.Google Scholar
Bhattacharyya, A., 1947. “On some Analogues of the Amount of Information and their Uses in Statistical Estimation”, Sankhya, VIII, 201–218.Google Scholar
Bhattacharyya, A., 1948. “On some Analogues of the Amount of Information and their Uses in Statistical Estimation”, Sankhya, VIII, 315–328.Google Scholar
Fisher, R. A., 1921. “Mathematical Foundations of Theoretical Statistics”, Phil. Trans. Roy. Soc., A, CCXXII, 309–368.Google Scholar