TITLE:
Generalized Method of Moments and Generalized Estimating Functions Based on Probability Generating Function for Count Models
AUTHORS:
Andrew Luong
KEYWORDS:
Mixture Distributions, Consistent Chi-Square Tests, Infinitely Divisible Distributions, Mixture Distributions, Distribution Free Test Statistics, Model Testing
JOURNAL NAME:
Open Journal of Statistics,
Vol.10 No.3,
June
11,
2020
ABSTRACT: 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.