A new improved Liu-type estimator for Poisson regression models

Year 2022, Volume: 51 Issue: 5, 1484 - 1503, 01.10.2022

Kadri Ulaş Akay , Esra Ertan

https://doi.org/10.15672/hujms.1012056

Cited By: 6

Abstract

The Poisson Regression Model (PRM) is commonly used in applied sciences such as economics and the social sciences when analyzing the count data. The maximum likelihood method is the well-known estimation technique to estimate the parameters in PRM. However, when the explanatory variables are highly intercorrelated, unstable parameter estimates can be obtained. Therefore, biased estimators are widely used to alleviate the undesirable effects of these problems. In this study, a new improved Liu-type estimator is proposed as an alternative to the other proposed biased estimators. The superiority of the new proposed estimator over the existing biased estimators is given under the asymptotic matrix mean square error criterion. Furthermore, Monte Carlo simulation studies are executed to compare the performances of the proposed biased estimators. Finally, the obtained results are illustrated in real data. Based on the set of experimental conditions which are investigated, the proposed biased estimator outperforms the other biased estimators.

Keywords

Poisson regression, mean squared error, multicollinearity, Ridge estimator, Liu estimator

References

• [1] M.M. Alanaz and Z.Y. Algamal, Proposed methods in estimating the ridge regression parameter in Poisson regression model, Electron. J. Appl. Stat. Anal. 11 (2), 506-515, 2018.
• [2] Z.Y. Algamal, Biased estimators in Poisson regression model in the presence of multicollinearity: a subject review, Al-Qadisiyah Journal for Administrative and Economic Sciences 20 (1), 37-43, 2018.
• [3] M.I. Alheety, M. Qasim, K. Månsson and B.M.G. Kibria, Modified almost unbiased two-parameter estimator for the Poisson regression model with an application to accident data, SORT 45 (2), 121-142, 2021.
• [4] A. Alkhateeb and Z.Y. Algamal, Jackknifed Liu-type estimator in Poisson regression model, J. Iran. Stat. Soc. (JIRSS) 19 (1), 21-37, 2020.
• [5] M. Amin, M.N. Akram and M. Amanullah, On the James-Stein estimator for the poisson regression model, Comm. Statist. Simulation Comput., Doi:10.1080/03610918.2020.1775851, 2020.
• [6] M. Amin, M.N. Akram and B.M.G. Kibria, A new adjusted Liu estimator for the Poisson regression model, Concurr Comput 33 (20), e6340, 2021.
• [7] Y. Asar and A. Genç, A new two-parameter estimator for the Poisson regression model, Iran. J. Sci. Technol. Trans. A: Sci. 42 (2), 793-803, 2018.
• [8] M.K. Çetinkaya and S. Kaçranlar, Improved two-parameter estimators for the negative binomial and Poisson regression models, J. Stat. Comput. Simul. 89 (14), 2645-2660, 2019.
• [9] P.K. Dunn and G.K. Smyth, Generalized Linear Models With Examples in R, Springer, New York, 2018.
• [10] R.W. Farebrother, Further results on the mean square error of Ridge regression, J. R. Stat. Soc. Ser. B. Stat. Methodol. 38 (3), 248-250, 1976.
• [11] J.M. Hilbe, Modeling Count Data, Cambridge University Press, Cambridge, 2014.
• [12] A.E. Hoerl and R.W. Kennard, Ridge regression: biased estimation for nonorthogonal problems, Technometrics 12 (1), 55-67, 1970.
• [13] N.H. Jadhav, A new linearized ridge Poisson estimator in the presence of multicollinearity, J. Appl. Stat. 49 (8), 2016-2034, 2022.
• [14] B.M.G. Kibria and A.F. Lukman, A new ridge-type estimator for the linear regression model: simulations and applications, Scientifica, Doi:10.1155/2020/9758378, 2020.
• [15] B.M.G. Kibria, K. Månsson and G. Shukur, Some ridge regression estimators for the zero-inflated Poisson model, J. Appl. Stat. 40 (4), 721-735, 2013.
• [16] B.M.G. Kibria, K. Månsson and G. Shukur, A simulation study of some biasing parameters for the ridge type estimation of Poisson regression, Comm. Statist. Simulation Comput. 44 (4), 943-957, 2015.
• [17] F.S. Kurnaz and K.U. Akay, A new Liu-type estimator, Statist. Papers 56 (2), 495- 517, 2015.
• [18] K. Liu, A new class of biased estimate in linear regression, Comm. Statist. Theory Methods 22 (2), 393-402, 1993.
• [19] K. Liu, Using Liu-type estimator to combat collinearity, Comm. Statist. Theory Methods 32 (5), 1009-1020, 2003.
• [20] A.F. Lukman, E. Adewuyi, K. Månsson and B.M.G. Kibria, A new estimator for the multicollinear Poisson regression model: simulation and application, Sci. Rep. 11 (1), 2021.
• [21] A.F. Lukman, B. Aladeitan, K. Ayinde and M.R. Abonazel, Modified ridge-type for the Poisson regression model: simulation and application, J. Appl. Stat. 49 (8), 2124- 2136, 2022.
• [22] K. Månsson, B.M.G. Kibria, P. Sjolander and G. Shukur, Improved Liu estimators for the Poisson regression model, Int. J. Probab. Stat. 1 (1), 2-6, 2012.
• [23] K. Månsson and B.M.G. Kibria, Estimating the Unrestricted and restricted Liu estimators for the Poisson regression model: method and application, Comput. Econ. 58 (2), 311-326, 2021.
• [24] K. Månsson and G. Shukur, A Poisson Ridge regression estimator, Econ. Model. 28 (4), 1475-1481, 2011.
• [25] R.H. Myers, D.C. Montgomery, G.G. Vining and T.J. Robinson, Generalized Linear Models: with Applications in Engineering and the Sciences, Wiley, New York, 2012.
• [26] M.R. Özkale and S. Kaçranlar, The restricted and unrestricted two-parameter estimators, Comm. Statist. Theory Methods 36 (15), 27072725, 2007.
• [27] M. Qasim, B.M.G. Kibria, K. Månsson and P. Sjölander, A new Poisson Liu regression estimator: method and application, J. Appl. Stat. 47 (12), 2258-2271, 2020.
• [28] M. Qasim, K. Månsson, M. Amin, B.M.G. Kibria and P. Sjölander, Biased adjusted Poisson Ridge estimators-method and application, Iran. J. Sci. Technol. Trans. A: Sci. 44 (6), 1775-1789, 2020.
• [29] N.K. Rashad and Z.Y. Algamal, A new Ridge estimator for the Poisson regression model, Iran. J. Sci. Technol. Trans. A: Sci. 43 (6), 2921-2928, 2019.
• [30] C.M. Theobald, Generalizations of mean square error applied to ridge regression, J. R. Stat. Soc. Ser. B. Stat. Methodol. 36 (1), 103-106, 1974.
• [31] S. Türkan and G. Özel, A new modified Jackknifed estimator for the Poisson regression model, J. Appl. Stat. 43 (10), 1892-1905, 2016.