Parameter estimation by Hellinger type distance for multivariate distributions based upon probability generating functions |
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Authors: | Choung Min Ng Seng-Huat Ong HM Srivastava |
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Institution: | 1. Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia;2. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3R4 |
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Abstract: | Maximum likelihood (ML) estimation is a popular method for parameter estimation when modeling discrete or count observations but unfortunately it may be sensitive to outliers. Alternative robust methods like minimum Hellinger distance (MHD) have been proposed for estimation. However, in the multivariate case, the MHD method leads to computer intensive estimation especially when the joint probability density function is complicated. In this paper, a Hellinger type distance measure based on the probability generating function is proposed as a tool for quick and robust parameter estimation. The proposed method yields consistent estimators, performs well for simulated and real data, and can be computationally much faster than ML or MHD estimation. |
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Keywords: | Bivariate negative binomial Consistency Maximum likelihood Penalized minimum generalized Hellinger distance Outliers Srivastava’s triple hypergeometric series |
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