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SOME METHODS FOR ESTIMATION IN

A NEGATIVE-BINOMIAL MODEL

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EIJI NAKASHIMA

*Department of Statistics, Radiation Effects Research Foundation,*

5-2 Hijiyama Park, Minami-ku, Hiroshima 732, Japan
(Received September 7, 1995; revised March 25, 1996)

**Abstract.**
To clarify the advantage of using the
quasilikelihood method, lack of robustness of the maximum likelihood
method was demonstrated for the negative-binomial model. Efficiency
calculations of the method of moments and the pseudolikelihood
method in the estimation of extra-Poisson parameters in a
negative-binomial model were carried out. Especially when the
overdispersion parameter is small, both methods are relatively
highly efficient and the pseudolikelihood estimate is more efficient
than the method of moments estimate. Two examples of the
quasilikelihood analyses of count data with overdispersion are
given. The bootstrap method also is applied to the data to
illustrate the advantage of the method of moments or
pseudolikelihood method in the estimation of the standard errors of
the mean parameter estimates under the negative-binomial model.

*Key words and phrases*:
Method of moments,
negative-binomial, overdispersion, pseudolikelihood,
quasilikelihood.

**Source**
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