Robust Estimates of the Negative Binomial Model

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Serval ID
serval:BIB_E3D166595E22
Type
Inproceedings: an article in a conference proceedings.
Publication sub-type
Abstract (Abstract): shot summary in a article that contain essentials elements presented during a scientific conference, lecture or from a poster.
Collection
Publications
Institution
Title
Robust Estimates of the Negative Binomial Model
Title of the conference
International conference on robust statistics (ICORS), 28 June - 2 July 2010 - Prague, Czech Republic
Author(s)
Amiguet M.
Publication state
Published
Issued date
2010
Language
english
Abstract
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
Create date
10/09/2015 14:16
Last modification date
20/08/2019 16:07
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