A New Kibria-Lukman-Type Estimator for Poisson Regression Models

Abstract

One of the most important models for the analysis of count data is the Poisson Regression Model (PRM). The parameter estimates of the PRM are obtained by the Maximum Likelihood Estimator (MLE). However, MLE is adversely affected in the presence of multicollinearity, which is known as the approximately linear relationship between the explanatory variables. Many shrinkage estimators have been proposed to reduce the effects of multicollinearity in PRMs. As an alternative to other biased estimators that are already in use in PRMs, we presented a novel estimator in this paper that is based on the Kibria-Lukman estimator. The superiority of the proposed new biased estimator over existing biased estimators is given by the asymptotic matrix mean square error. Furthermore, two separate Monte Carlo simulation studies are conducted to investigate the performance of the proposed biased estimators. Finally, real data is used to examine the superiority of the proposed estimator.

Keywords

• Mean squared error
• multicollinearity
• poisson liu estimator
• poisson regression
• poisson ridge estimator

References

1. Akay, K. U., Ertan, E., & Erkoç, A. (2023). A New biased estimator and variations based on the Kibria Lukman Estimator. Istanbul Journal of Mathematics, 1(2), 74-85. google scholar
2. Akay, K. U., & Ertan, E., (2022). A new Liu-type estimator in Poisson regression models. Hacet JMath Stat, 51 (5), 1484-1503. google scholar
3. Aladeitan, B. B., Adebimpe, O., Lukman, A. F., Oludoun, O., & Abiodun, O. E. (2021). Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation. F1000Research, 10. google scholar
4. Alanaz, M. M., & Algamal, Z. Y., (2018). Proposed methods in estimating the ridge regression parameter in Poisson regression model. Electronic Journal of Applied Statistical Analysis, 11(2), 506-515. google scholar
5. Algamal, Z. Y. (2018). 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. google scholar
6. Alheety, M. I., Qasim, M., Mânsson, K., & Kibria, B. G. (2021). Modified almost unbiased two-parameter estimator for the Poisson regression model with an application to accident data. SORT, 121-142. google scholar
7. Alkhateeb, A., & Algamal, Z. (2020). Jackknifed Liu-type estimator in Poisson regression model. Journal of The Iranian Statistical Society, 19(1), 21-37. google scholar
8. Amin, M., Akram, M. N., & Amanullah, M. (2022). On the James-Stein estimator for the Poisson regression model. Communications in Statistics-Simulation and Computation, 51(10), 5596-5608. google scholar

9. Amin, M., Akram, M. N., & Kibria, B. G. (2021). A new adjusted Liu estimator for the Poisson regression model. Concurrency and Computation: Practice and Experience, 33(20), e6340. google scholar
10. Alrweili, H. (2024). Kibria-Lukman Hybrid Estimator for Handling Multicollinearity in Poisson Regression Model: Method and Application. International Journal of Mathematics and Mathematical Sciences, 2024(1), 1053397. google scholar
11. Asar, Y., & Genç, A. (2018). A new two-parameter estimator for the poisson regression model. Iranian Journal of Science and Technology, Transactions A: Science, 42(2), 793-803. google scholar
12. Çetinkaya, M. K., & Kaçıranlar, S. (2019). Improved two-parameter estimators for the negative binomial and Poisson regression models. Journal of Statistical Computation and Simulation, 89(14), 2645-2660. google scholar
13. Dawoud, I., Abonazel, M. R., & Awwad, F. A. (2022). Generalized Kibria-Lukman estimator: Method, simulation, and application. Frontiers in Applied Mathematics and Statistics, 8, 880086. google scholar
14. Dunn, P. K., & Smyth, G. K. (2018). Generalized Linear Models With Examples in R. Springer, New York, NY. google scholar
15. Ertan, E., & Akay, K. U. (2023). A new class of Poisson-ridge-type estimator. Scientific Reports, 13(1), 4968. google scholar
16. Farebrother, R.W. (1976). Further results on the mean square error of ridge regression. JR Stat Soc B, (28), 248-250. google scholar
17. Hardin, J. W., & Hilbe, J. M. (2018). Generalized linear models and extensions. Fourth edition. Stata press. google scholar
18. Hilbe, J. M. (2014). Modeling Count Data; Cambridge University Press: Cambridge. google scholar
19. Hoerl, A.E., & Kennard, R.W. (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67. google scholar
20. Jadhav, N. H. (2022). A new linearized ridge Poisson estimator in the presence of multicollinearity. Journal of Applied Statistics, 49(8), 2016-2034. google scholar
21. Kibria, B. M. G., Mânsson, K., & Shukur, G. (2013). Some ridge regression estimators for the zero-inflated Poisson model. Journal of Applied Statistics, 40(4), 721-735. google scholar
22. Kibria B. M. G., Mânsson K., & Shukur, G. (2015). A simulation study of some biasing parameters for the ridge type estimation of Poisson regression. Commun Stat Simul Comput, 44(4), 943-957. google scholar
23. Kurnaz, F. S., & Akay, K. U. (2015). A new Liu-type estimator. Stat Papers, 56, 495-517. google scholar
24. Liu, K. (1993). A new class of biased estimate in linear regression. Commun Stat Theory Methods 22(2): 393-402. google scholar
25. Liu, K. (2003). Using Liu-type estimator to combat collinearity. Commun Stat Theory Methods 32(5):1009-1020. google scholar
26. Lukman, A. F., Adewuyi, E., Mânsson, K., & Kibria, B. G. (2021). A new estimator for the multicollinear Poisson regression model: simulation and application. Scientific Reports, 11(1), 3732. google scholar
27. Lukman, A. F., Aladeitan, B., Ayinde, K., & Abonazel, M. R. (2022). Modified ridge-type for the Poisson regression model: simulation and application. Journal of Applied Statistics, 49(8), 2124-2136. google scholar
28. Lukman, A. F., Allohibi, J., Jegede, S. L., Adewuyi, E. T., Oke, S., & Alharbi, A. A. (2023). Kibria-Lukman-Type Estimator for Regularization and Variable Selection with Application to Cancer Data. Mathematics, 11(23), 4795. google scholar
29. Mânsson, K., & Shukur, G. (2011). A Poisson ridge regression estimator. Economic Modelling, 28(4), 1475-1481. google scholar
30. Mânsson, K., Kibria, B. G., Sjolander, P., & Shukur, G. (2012). Improved Liu estimators for the Poisson regression model. International Journal of Statistics and Probability, 1(1), 2-6. google scholar
31. Mânsson, K., & Kibria, B. G. (2020). Estimating the Unrestricted and Restricted Liu Estimators for the Poisson Regression Model: Method and Application. Computational Economics, 1-16. google scholar
32. McDonald, G. C., & Galarneau, D. I. (1975) A Monte Carlo evaluation of some ridge-type estimators. JAm Stat Assoc, 70(350), 407-416. google scholar
33. Myers, R. H., Montgomery, D. C., Vining, G. G., & Robinson, T. J. (2012). Generalized linear models: with applications in engineering and the sciences, Wiley, New York. google scholar
34. Özkale, M. R., & Kaçıranlar, S. (2007). The restricted and unrestricted two-parameter estimators. Commun Stat Theory Methods, 36, 2707-2725. google scholar
35. Qasim, M., Kibria, B. M. G., Mânsson, K., & Sjölander, P. (2020a). A new Poisson-Liu Regression Estimator: method and application. Journal of Applied Statistics, 47(12), 2258-2271. google scholar
36. Qasim, M., Mânsson, K., Amin, M., Kibria, B. G., & Sjölander, P. (2020b). Biased adjusted Poisson ridge estimators-method and application. Iranian Journal of Science and Technology, Transactions A: Science, 44(6), 1775-1789. google scholar
37. Rashad, N. K., & Algamal, Z. Y. (2019). A New Ridge Estimator for the Poisson Regression Model. Iranian Journal of Science and Technology, Transactions A: Science, 43(6), 2921-2928. google scholar
38. Theobald, C.M. (1974) Generalizations of mean square error applied to ridge regression. JR Stat So B 36: 103-106. google scholar
39. Türkan, S., & Özel, G. (2016). A new modified Jackknifed estimator for the Poisson regression model. Journal of Applied Statistics, 43(10), 1892-1905. google scholar