Robust fitting of the binomial model
Robust fitting of the binomial model
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.
bias, breakdown point, e-estimation, influence function, likelihood disparity, m-estimation, minimum disparity estimation, optimal MGP estimation
1117-1136
Ruckstuhl, A.F.
8405a5e0-ba61-4ff4-b288-96c8acb35ba3
Welsh, A.H.
27640871-afff-4d45-a191-8a72abee4c1a
2001
Ruckstuhl, A.F.
8405a5e0-ba61-4ff4-b288-96c8acb35ba3
Welsh, A.H.
27640871-afff-4d45-a191-8a72abee4c1a
Ruckstuhl, A.F. and Welsh, A.H.
(2001)
Robust fitting of the binomial model.
Annals of Statistics, 29 (4), .
Abstract
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.
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Published date: 2001
Keywords:
bias, breakdown point, e-estimation, influence function, likelihood disparity, m-estimation, minimum disparity estimation, optimal MGP estimation
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Statistics
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Local EPrints ID: 29935
URI: http://eprints.soton.ac.uk/id/eprint/29935
PURE UUID: 7a8cc791-f0cf-4775-937f-c7a37979f056
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Date deposited: 11 May 2006
Last modified: 08 Jan 2022 15:53
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Author:
A.F. Ruckstuhl
Author:
A.H. Welsh
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