Author: Andrew Luong
Generalized method of moments based on probability generating function is considered. Estimation and model testing are unified using this approach which also leads to distribution free chi-square tests. The estimation methods developed are also related to estimation methods based on generalized estimating equations but with the advantage of having statistics for model testing. The methods proposed overcome numerical problems often encountered when the probability mass functions have no closed forms which prevent the use of maximum likelihood (ML) procedures and in general, ML procedures do not lead to distribution free model testing statistics.
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