Open Access
August 2001 Robust fitting of the binomial model
A. F. Ruckstuhl, A. H. Welsh
Ann. Statist. 29(4): 1117-1136 (August 2001). DOI: 10.1214/aos/1013699996


We consider the problem of robust inference for the binomial $(m, \pi)$ model. The discreteness of the data and the fact that the parameter and sample spaces are bounded mean that standard robustness theory gives surprising results. For example, the maximum likelihood estimator (MLE) is quite robust, it cannot be improved on for $m=1$ but can be for $m>1$. We discuss four other classes of estimators: $M$-estimators, minimum disparity estimators, optimal MGP estimators, and a new class of estimators which we call $E$-estimators. We show that $E$-estimators have a non-standard asymptotic theory which challenges the accepted relationships between robustness concepts and thereby provides new perspectives on these concepts.


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A. F. Ruckstuhl. A. H. Welsh. "Robust fitting of the binomial model." Ann. Statist. 29 (4) 1117 - 1136, August 2001.


Published: August 2001
First available in Project Euclid: 14 February 2002

zbMATH: 1041.62019
MathSciNet: MR1869243
Digital Object Identifier: 10.1214/aos/1013699996

Primary: 62F12 , 62F35

Keywords: bias , Breakdown point , E-estimation, , influence function , likelihood disparity , M-estimation , minimum disparity estimation , optimal MGP estimation

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.29 • No. 4 • August 2001
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