Parameter Estimation for Generalized Poisson Regression Model
Abstract
The purpose of this study was to compare parameter estimation methods for generalized poisson regression model which the independent variable was normal distributed with mean equal to 0 and standard deviation equal to 1. The coefficients of regression and dispersion parameter were estimated by four estimation methods: maximum likelihood estimation (MLE), jackknife maximum likelihood estimation (JMLE), moment estimation (ME) and jackknife moment estimation (JME). The data was generated by using Monte-Carlo simulation method with the repetition of 1,000 times, sample sizes are equal to 20, 50, 100 and 300: is equal to 0, are equal to -0.5, -0.3, 0.3 and 0.5 and the dispersion parameters are equal to -0.5, -0.3, 0, 0.3 and 0.5. The sum of mean squares error and the sum of bias were used as the performance criteria. The simulation study indicated that the efficiency of the maximum likelihood estimation was not different from the jackknife maximum likelihood estimation. As well as the jackknife moment estimation was not different from the moment estimation. Therefore, the moment estimation was more appropriate than the maximum likelihood estimation for the underdispersion situation while the maximum likelihood estimation was more appropriate than the moment estimation for the overdispersion situation. The moment estimation and the maximum likelihood estimation were appropriate for equidispersion situation. Keywords : generalized poisson regression model, jackknife method, underdispersion, equidispersion, overdispersionReferences
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Casella, G., Berger, R.L. (2002). Statistical Inference. California: Duxbury.
Esemokumo, P.A., Rebecca, B. & Idochi, O. (2015). Jackknife Algorithm on Linear Regression Estimation. International Journal for Research in Mathematics and Statistics, 1(1), 34-40.
Gould, W., Sribney W. (1999). Maximum likelihood estimation with stata. College station, Tex: Stata press.
Islam, M.M., Alam, M., Tariquzaman, Md., Kabir, M.A., Pervin, R., Begum, & Khan, Md. M. H. (2013).
Predictors of the number of under-five malnourished children in Bangladesh: application of the generalized poisson regression model. BMC Public Health, 13.
Ismail, N., Jemain, A. A. (2007). Handling Overdispersion with Negative Binomial and Generalized Poisson Regression Models. Casualty Actuarial Society Forum, 103-158.
McCullagh, P., Nelder, J.A. (1952). Generalized Linear Models. Chapman&Hall/CRC.
Miller, R.G. (1974). The Jackknife--A Review. Biometrika, 60(1), 1-15.
Sahai, H., Khurshid, A. (2001). Pocket Dictionary of Statistics. McGraw-Hill/Irwin.
Singh, K.P., Wulu, J.T. & Bartolucci, A.A. (2004). A note on Generalized Poisson Regression Model.
Journal of the Royal Statistical, 2029-2034
Türkan, S., Özel, G. (2017). A Jackknifed estimators for the negative binomial. Communications in
Statistics - Simulation and Computation, 1-21.
Wagh, Y.S., Kamalja, K.K. (2017). Modelling Auto Insurance Claims in Singapore. Sri Lankan Journal of Applied Statistics, 18(2), 105-118.
Zamani, H., Ismail, N. (2012). Functional Form for the Generalized Poisson Regression Model. Communications in Statistics - Theory and Methods, 3666-3675.
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Published
2019-10-03
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Research Article
