The Annals of Statistics

Robust fitting of the binomial model

A. F. Ruckstuhl and A. H. Welsh

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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.

Article information

Ann. Statist., Volume 29, Number 4 (2001), 1117-1136.

First available in Project Euclid: 14 February 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F12: Asymptotic properties of estimators 62F35: Robustness and adaptive procedures

Bias breakdown point E-estimation, influence function likelihood disparity M-estimation minimum disparity estimation optimal MGP estimation


Ruckstuhl, A. F.; Welsh, A. H. Robust fitting of the binomial model. Ann. Statist. 29 (2001), no. 4, 1117--1136. doi:10.1214/aos/1013699996.

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