Parameter estimation by Hellinger type distance for multivariate distributions based upon probability generating functions

• Published in: Applied mathematical modelling Vol. 37; no. 12-13; pp. 7374 - 7385
• Main Authors: Ng, Choung Min, Ong, Seng-Huat, Srivastava, H.M.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.07.2013
• Subjects: Bivariate negative binomial; Computer simulation; Consistency; Counting; Magnetohydrodynamics; Mathematical analysis; Mathematical models; Maximum likelihood; MHD; Outliers; Parameter estimation; Penalized minimum generalized Hellinger distance; Srivastava’s triple hypergeometric series; Outliers; Bivariate negative binomial; Maximum likelihood; Srivastava’s triple hypergeometric series; Penalized minimum generalized Hellinger distance; Consistency
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2013.02.044

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.