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.
|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
|Date Deposited:||11 May 2006|
|Last Modified:||31 May 2011 23:52|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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