Robust Estimates of the Negative Binomial Model

TitreRobust Estimates of the Negative Binomial Model
Publication TypeConference Paper
Year of Publication2010
AuthorsAmiguet, M
Conference NameInternational conference on robust statistics (ICORS)
PublisherInternational conference on robust statistics (ICORS)
Conference LocationPrague, Czech Republic
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 [5].

References:
[1] A. Marazzi and C. Ruffieux. The Truncated Mean of an Asymmetric Distribution. Computational Statistics f3 Data Analysis, 32, 79-100, 1999.
[2] D. Gervini and V.J. Yohai. A class of robust and fully efficient regression estimates. The Annals of Statistics, 30(2), 583-616, 2002.
[3] A. Marazzi and V.J. Yohai. Adaptively truncated maximum likelihood regression with asymmetric errors. Journal of statistical planning and inference, 122, 271-291, 2004.
[4] B. G. Lindsay. Efficiency versus robustness: The Case for Minimum Hellinger Distance and Related Methods. Ann. Statist., 22, 1081-1114, 1994.
[5] V. J. Yohai and A. Marazzi. Optimal Robust Estimates Using the Hellinger Distance. Advances in Data Analysis and Classification, In press.

Notes

28 June - 2 July 2010 - Prague, Czech Republic

URLhttp://centrumjh.karlin.mff.cuni.cz/icors2010web.pdf
Citation Key / SERVAL ID6222

                         

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