246
Views
4
CrossRef citations to date
0
Altmetric
Article

Ridge estimator in a mixed Poisson regression model

ORCID Icon & ORCID Icon
Pages 3253-3270 | Received 31 Jan 2022, Accepted 29 Jun 2022, Published online: 18 Jul 2022

References

  • Altun, E. 2019. A new model for over-dispersed count data: Poisson quasi-Lindley regression model. Mathematical Sciences 13 (3):241–7. doi:10.1007/s40096-019-0293-5.
  • Cameron, A. C., and P. K. Trivedi. 2013. Regression analysis of count data. 2nd ed. France: Cambridge University Press.
  • Dutang, C. 2017. Some explanations about the IWLS algorithm to fit generalized linear models. hal-01577698.
  • Farebrother, R. 1976. Further results on the mean square error of ridge regression. Journal of the Royal Statistical Society. Series B (Methodological) 38 (3):248–50. https://www.jstor.org/stable/2984971. doi:10.1111/j.2517-6161.1976.tb01588.x.
  • Greenwood, M., and G. U. Yule. 1920. An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents. Journal of the Royal Statistical Society 83 (2):255–79. doi:10.2307/2341080.
  • Hoerl, A. E., and R. W. Kennard. 1970a. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12 (1):55–67. doi:10.2307/1271436.
  • Hoerl, A. E., and R. W. Kennard. 1970b. Ridge regression: Application to non-orthogonal problems. Technometrics 12 (1):69–82. doi:10.2307/1267352.
  • Khalaf, G., and G. Shukur. 2005. Choosing ridge parameters for regression problems. Communications in Statistics - Theory and Methods 34 (5):1177–82. doi:10.1081/STA-200056836.
  • Kibria, B. M. 2003. Performance of some new ridge regression estimators. Communications in Statistics - Simulation and Computation 32 (2):419–35. doi:10.1081/SAC-120017499.
  • Kibria, G. B. M., and A. F. Lukman. 2020. A new ridge-type estimator for the linear regression model: Simulations and applications. Scientifica 2020:9758378. doi:10.1155/2020/9758378.
  • Liu, K. 1993. A new class of biased estimate in linear regression. Communications in Statistics- Theory and Methods 22:393–402. doi:10.1080/03610929308831027.
  • Liu, K. 2003. Using Liu-type estimator to combat collinearity. Communications in Statistics - Theory and Methods 32 (5):1009–20. doi:10.1081/STA-120019959.
  • Månsson, K. 2012. On ridge estimators for the negative binomial regression model. Economic Modelling 29 (2):178–84. doi:10.1016/j.econmod.2011.09.009.
  • Månsson, K., and G. Shukur. 2011. A Poisson ridge regression estimator. Economic Modelling 28 (4):1475–81. doi:10.1016/j.econmod.2011.02.030.
  • McDonald, G. C., and D. I. Galarneau. 1975. A Monte Carlo evaluation of some ridge-type estimators. Journal of the American Statistical Association 70 (350):407–16. doi:10.2307/2285832.
  • Muniz, G., and B. M. G. Kibria. 2009. On some ridge regression estimators: An empirical comparisons. Communications in Statistics - Simulation and Computation 38 (3):621–30. doi:10.1080/03610910802592838.
  • Newhouse, P., and S. D. Oman. 1971. An evaluation of ridge estimators. RAND Corporation Santa Monica.
  • Nomura, M. 1988. On the almost unbiased ridge regression estimation. Communications in Statistics - Simulation and Computation 17 (3):729–43. doi:10.1080/03610918808812690.
  • Qasim, M., B. M. G. Kibria, K. Månsson, and P. Sjolander. 2019. A new Poisson Liu regression estimator: Method and application. Journal of Applied Statistics 47:258–2271. doi:10.1080/02664763.2019.1707485.
  • Schaefer, R. L., L. D. Roi, and R. A. Wolfe. 1984. A ridge logistic estimator. Communications in Statistics - Theory and Methods 13 (1):99–113. doi:10.1080/03610928408828664.
  • Segerstedt, B. 1992. On ordinary ridge regression in generalized linear models. Communications in Statistics - Theory and Methods 21 (8):2227–46. doi:10.1080/03610929208830909.
  • Shoukri, M. M., M. H. Asyali, R. VanDorp, and D. Kelton. 2021. The Poisson inverse Gaussian regression model in the analysis of clustered counts data. Journal of Data Science 2 (1):17–32. doi:10.6339/JDS.2004.02(1).135.
  • Tharshan, R., and P. Wijekoon. 2021. A modification of the Quasi Lindley distribution. Open Journal of Statistics 11 (3):369–92. doi:10.4236/ojs.2021.113022.
  • Tharshan, R., and P. Wijekoon. 2022a. A new mixed Poisson distribution for over-dispersed count data: Theory and applications. Reliability: Theory and Applications 17:33–51. http://www.gnedenko.net/RTA/index.php/rta/article/view/842.
  • Tharshan, R., and P. Wijekoon. 2022b. Poisson-modification of Quasi Lindley regression model for over-dispersed count responses. Communications in Statistics - Simulation and Computation: 1–16. doi:10.1080/03610918.2022.2044052.
  • Türkan, S., and G. Özel. 2016. A new modified Jackknifed estimator for the Poisson regression model. Journal of Applied Statistics 43 (10):1892–905. doi:10.1080/02664763.2015.1125861.
  • Wongrin, W., and W. Bodhisuwan. 2017. Generalized Poisson-Lindley linear model for count data. Journal of Applied Statistics 44 (15):2659–71. doi:10.1080/02664763.2016.1260095.
  • Zamani, H., N. Ismail, and P. Faroughi. 2014. Poisson-weighted exponential univariate version and regression model with applications. Journal of Mathematics and Statistics 10 (2):148–54. doi:10.3844/jmssp.2014.148.154.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.