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Simulated Minimum Hellinger Distance Inference Methods for Count Data

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Document pages: 33 pages

Abstract: In this paper, we consider simulated minimum Hellinger distance (SMHD)inferences for count data. We consider grouped and ungrouped data and emphasizeSMHD methods. The approaches extend the methods based on the deterministicversion of Hellinger distance for count data. The methods are general, it onlyrequires that random samples from the discrete parametric family can be drawnand can be used as alternative methods to estimation using probabilitygenerating function (pgf) or methods based matching moments. Whereasthis paper focuses on count data, goodness of fit tests based on simulatedHellinger distance can also be applied for testing goodness of fit for continuousdistributions when continuous observations are grouped into intervals like inthe case of the traditional Pearson’s statistics. Asymptoticproperties of the SMHD methods are studied and the methods appear to preservethe properties of having good efficiency and robustness of the deterministicversion.

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