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Biometrika 1983 70(1):269-274; doi:10.1093/biomet/70.1.269
© 1983 by Biometrika Trust
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Some remarks on overdispersion

D. R. COX

Department of Mathematics, Imperial College London

It is shown that maximum likelihood estimation of a simple model retains high efficiency in the presence of modest amounts of overdispersion. The main requirement is that the target parameter should be the moment parameter of an exponential family distribution, or more generally of a parameter for which the order n–1 bias of the maximum likelihood estimate is zero. Extensions for models with explanatory variables are outlined.

Key Words: Asymptotic theory • Dispersion test • Exponential distribution • Maximum likelihood • Negative binomial distribution • Pareto distribution • Poisson distribution • Quasilikelihood


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