Robust fitting of the binomial model

Ruckstuhl, A.F. and Welsh, A.H. (2001) Robust fitting of the binomial model. Annals of Statistics, 29, (4), 1117-1136.


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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 relationship between robustness concepts and thereby provided new perspectives on these concepts.

Item Type: Article
Related URLs:
Keywords: bias, breakdown point, e-estimation, influence function, likelihood disparity, m-estimation, minimum disparity estimation, optimal MGP estimation
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Statistics
ePrint ID: 29935
Accepted Date and Publication Date:
Date Deposited: 11 May 2006
Last Modified: 31 Mar 2016 11:56

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