TITLE:
Simulated Minimum Hellinger Distance Inference Methods for Count Data
AUTHORS:
Andrew Luong, Claire Bilodeau, Christopher Blier-Wong
KEYWORDS:
Break Down Points, Robustness, Power Mixture, Esscher Transform, Mixture Discrete Distributions, Chi-Square Tests Statistics
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.1,
February
28,
2018
ABSTRACT: 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.