The Annals of Mathematical Statistics

On Small-Sample Estimation

George W. Brown

Full-text: Open access

Abstract

This paper discusses some of the concepts underlying small sample estimation and reexamines, in particular, the current notions on "unbiased" estimation. Alternatives to the usual unbiased property are examined with respect to invariance under simultaneous one-to-one transformation of parameter and estimate; one of these alternatives, closely related to the maximum likelihood method, seems to be new. The property of being unbiased in the likelihood sense is essentially equivalent to the statement that the estimate is a maximum likelihood estimate based on some distribution derived by integration from the original sampling distribution, by virtue of a "hereditary" property of maximum likelihood estimation. An exposition of maximum likelihood estimation is given in terms of optimum pairwise selection with equal weights, providing a type of rationale for small sample estimation by maximum likelihood.

Article information

Source
Ann. Math. Statist. Volume 18, Number 4 (1947), 582-585.

Dates
First available: 28 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoms/1177730349

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoms/1177730349

Mathematical Reviews number (MathSciNet)
MR22337

Zentralblatt MATH identifier
0029.40701

Citation

Brown, George W. On Small-Sample Estimation. The Annals of Mathematical Statistics 18 (1947), no. 4, 582--585. doi:10.1214/aoms/1177730349. http://projecteuclid.org/euclid.aoms/1177730349.


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