The Annals of Mathematical Statistics

Unbiased Estimation of Location and Scale Parameters

J. K. Ghosh and Rajinder Singh

Full-text: Open access

Abstract

It is well-known that there is a close connection between linear functionals on an appropriate Banach space and unbiased estimators. In Section 2 we prove some results concerning unbiased estimation of location and scale parameters. As application of these results we consider the case of Cauchy density with unknown location [scale] but known scale [location] parameter. We show that there exists no unbiased estimator for the location parameter, and none with finite variance for the scale parameters. If the Cauchy density involves both location and scale parameters, then it is shown that neither of these parameters has an unbiased estimator. Some information about other parametric functions is also given. The present results for the location parameter case were obtained previously by H. Pollard; we are grateful to Professor Kiefer for informing us of Pollard's work.

Article information

Source
Ann. Math. Statist., Volume 37, Number 6 (1966), 1671-1675.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177699155

Digital Object Identifier
doi:10.1214/aoms/1177699155

Mathematical Reviews number (MathSciNet)
MR202238

Zentralblatt MATH identifier
0146.40001

JSTOR
links.jstor.org

Citation

Ghosh, J. K.; Singh, Rajinder. Unbiased Estimation of Location and Scale Parameters. Ann. Math. Statist. 37 (1966), no. 6, 1671--1675. doi:10.1214/aoms/1177699155. https://projecteuclid.org/euclid.aoms/1177699155


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