The Annals of Mathematical Statistics

Minimum Variance Estimation Without Regularity Assumptions

Douglas G. Chapman and Herbert Robbins

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Abstract

Following the essential steps of the proof of the Cramer-Rao inequality [1, 2] but avoiding the need to transform coordinates or to differentiate under integral signs, a lower bound for the variance of estimators is obtained which is (a) free from regularity assumptions and (b) at least equal to and in some cases greater than that given by the Cramer-Rao inequality. The inequality of this paper might also be obtained from Barankin's general result [3]. Only the simplest case--that of unbiased estimation of a single real parameter--is considered here but the same idea can be applied to more general problems of estimation.

Article information

Source
Ann. Math. Statist. Volume 22, Number 4 (1951), 581-586.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoms/1177729548

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoms/1177729548

Mathematical Reviews number (MathSciNet)
MR44084

Zentralblatt MATH identifier
0044.34302

Citation

Chapman, Douglas G.; Robbins, Herbert. Minimum Variance Estimation Without Regularity Assumptions. The Annals of Mathematical Statistics 22 (1951), no. 4, 581--586. doi:10.1214/aoms/1177729548. http://projecteuclid.org/euclid.aoms/1177729548.


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