Robust Estimates of the Negative Binomial Model
Détails
ID Serval
serval:BIB_E3D166595E22
Type
Actes de conférence (partie): contribution originale à la littérature scientifique, publiée à l'occasion de conférences scientifiques, dans un ouvrage de compte-rendu (proceedings), ou dans l'édition spéciale d'un journal reconnu (conference proceedings).
Sous-type
Abstract (résumé de présentation): article court qui reprend les éléments essentiels présentés à l'occasion d'une conférence scientifique dans un poster ou lors d'une intervention orale.
Collection
Publications
Institution
Titre
Robust Estimates of the Negative Binomial Model
Titre de la conférence
International conference on robust statistics (ICORS), 28 June - 2 July 2010 - Prague, Czech Republic
Statut éditorial
Publié
Date de publication
2010
Langue
anglais
Résumé
We consider robust parametric procedures for univariate discrete distributions, focusing on the negative binomial model. The procedures are based on three steps:
?First, a very robust, but possibly inefficient, estimate of the model parameters is computed.
?Second, this initial model is used to identify outliers, which are then removed from the sample.
?Third, a corrected maximum likelihood estimator is computed with the remaining observations.
The final estimate inherits the breakdown point (bdp) of the initial one and its efficiency can be significantly higher. Analogous procedures were proposed in [1], [2], [5] for the continuous case.
A comparison of the asymptotic bias of various estimates under point contamination points out the minimum Neyman's chi-squared disparity estimate as a good choice for the initial step. Various minimum disparity estimators were explored by Lindsay [4], who showed that the minimum Neyman's chi-squared estimate has a 50% bdp under point contamination; in addition, it is asymptotically fully efficient at the model. However, the finite sample efficiency of this estimate under the uncontaminated negative binomial model is usually much lower than 100% and the bias can be strong. We show that its performance can then be greatly improved using the three step procedure outlined above. In addition, we compare the final estimate with the procedure described in
?First, a very robust, but possibly inefficient, estimate of the model parameters is computed.
?Second, this initial model is used to identify outliers, which are then removed from the sample.
?Third, a corrected maximum likelihood estimator is computed with the remaining observations.
The final estimate inherits the breakdown point (bdp) of the initial one and its efficiency can be significantly higher. Analogous procedures were proposed in [1], [2], [5] for the continuous case.
A comparison of the asymptotic bias of various estimates under point contamination points out the minimum Neyman's chi-squared disparity estimate as a good choice for the initial step. Various minimum disparity estimators were explored by Lindsay [4], who showed that the minimum Neyman's chi-squared estimate has a 50% bdp under point contamination; in addition, it is asymptotically fully efficient at the model. However, the finite sample efficiency of this estimate under the uncontaminated negative binomial model is usually much lower than 100% and the bias can be strong. We show that its performance can then be greatly improved using the three step procedure outlined above. In addition, we compare the final estimate with the procedure described in
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10/09/2015 14:16
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