Conditional inference on a mixture model for the analysis of count data

Abstract

In this paper we examine estimation in a mixture model under various assumptions for the underlying distribution. We suggest that statistical inference should be carried out using the conditional distribution given the appropriate ancillary statistics. The conditional likelihood approach used here can be justified by Cox's (1958) criterion about ancillarity in the presence of a nuisance parameter, and in the spirit of Godambe's (1976) conditional likelihood optimum estimating equation. The analysis is known to be easier and more stable than the unconditional likelihood function approach. The probability distributions in the analysis of count data discussed here include Poisson, binomial, geometric and negative binomial distributions. The information loss incurred by using the conditional approach is discussed