The Annals of Statistics

A Necessary and Sufficient Condition for Second Order Admissibility with Applications to Berkson's Bioassay Problem

J. K. Ghosh and Bimal K. Sinha

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Abstract

A theorem is proved which gives a necessary and sufficient condition for improving, up to $o(n^{-2})$, the mean squared error of the maximum likelihood estimate $\hat{\theta}$ by using an estimate of the form $\hat{\theta} + d(\hat{\theta})/n$. An application is made to a bioassay problem of Berkson.

Article information

Source
Ann. Statist., Volume 9, Number 6 (1981), 1334-1338.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345650

Digital Object Identifier
doi:10.1214/aos/1176345650

Mathematical Reviews number (MathSciNet)
MR630116

Zentralblatt MATH identifier
0484.62047

JSTOR
links.jstor.org

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 62C15: Admissibility

Keywords
Maximum likelihood estimate second order admissibility

Citation

Ghosh, J. K.; Sinha, Bimal K. A Necessary and Sufficient Condition for Second Order Admissibility with Applications to Berkson's Bioassay Problem. Ann. Statist. 9 (1981), no. 6, 1334--1338. doi:10.1214/aos/1176345650. https://projecteuclid.org/euclid.aos/1176345650


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Corrections

  • See Correction: Linda June Davis. Correction: Comments on a Paper by T. Amemiya on Estimation in a Dichotomous Logit Regression Model. Ann. Statist., vol. 13, no. 4 (1985), 1629.