Parameter estimation by Hellinger type distance for multivariate distributions based upon probability generating functions
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 multivar...
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| Published in | Applied mathematical modelling Vol. 37; no. 12-13; pp. 7374 - 7385 |
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| Format | Journal Article |
| Language | English |
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01.07.2013
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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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| AbstractList | 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. |
| Author | Ng, Choung Min Ong, Seng-Huat Srivastava, H.M. |
| Author_xml | – sequence: 1 givenname: Choung Min surname: Ng fullname: Ng, Choung Min email: ngcm@um.edu.my organization: Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia – sequence: 2 givenname: Seng-Huat surname: Ong fullname: Ong, Seng-Huat email: ongsh@um.edu.my organization: Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia – sequence: 3 givenname: H.M. surname: Srivastava fullname: Srivastava, H.M. email: harimsri@math.uvic.ca organization: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3R4 |
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| Cites_doi | 10.2307/2348162 10.1016/j.spl.2007.01.014 10.1016/j.apm.2011.02.047 10.1080/03610919908813547 10.1080/01621459.1961.10480641 10.1017/S0305004100041359 10.1111/1467-9884.00325 10.1080/03610910903443980 10.1111/j.2517-6161.1973.tb00945.x 10.1080/01621459.1987.10478501 10.1109/TR.2007.896757 10.1214/aos/1176343842 10.1080/01621459.1972.10481302 10.1080/03610919708813381 10.1137/1012102 10.1080/03610919208813020 |
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| Keywords | Outliers Bivariate negative binomial Maximum likelihood Srivastava’s triple hypergeometric series Penalized minimum generalized Hellinger distance Consistency |
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| SubjectTerms | 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 |
| Title | Parameter estimation by Hellinger type distance for multivariate distributions based upon probability generating functions |
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