Author(s)

Andrew Luong, Claire Bilodeau, Christopher Blier-Wong

école d’actuariat, Université Laval, Québec, Canada.

In this paper, we consider simulated minimum Hellinger distance (SMHD) inferences for count data. We consider grouped and ungrouped data and emphasize SMHD methods. The approaches extend the methods based on the deterministic version of Hellinger distance for count data. The methods are general, it only requires that random samples from the discrete parametric family can be drawn and can be used as alternative methods to estimation using probability generating function (pgf) or methods based matching moments. Whereas this paper focuses on count data, goodness of fit tests based on simulated Hellinger distance can also be applied for testing goodness of fit for continuous distributions when continuous observations are grouped into intervals like in the case of the traditional Pearson’s statistics. Asymptotic properties of the SMHD methods are studied and the methods appear to preserve the properties of having good efficiency and robustness of the deterministic version.

Break Down Points, Robustness, Power Mixture, Esscher Transform, Mixture Discrete Distributions, Chi-Square Tests Statistics

Luong, A. , Bilodeau, C. and Blier-Wong, C. (2018) Simulated Minimum Hellinger Distance Inference Methods for Count Data. Open Journal of Statistics, 8, 187-219. doi: 10.4236/ojs.2018.81012.