Liu-Type estimator in gamma regression model based on (r-(k-d)) class estimator

Document Type : Research Paper


1 College of Physical Education and Sport Sciences, University of Samarra, Salah Aldeen, Iraq

2 Department of Statistics and Informatics, University of Mosul, Iraq


It is known that when the multicollinearity exists in the gamma regression model, the variance of maximum likelihood estimator is unstable and high. In this article, a new Liu-type estimator based on (r-(k-d)) class estimator in gamma regression model is proposed. The performance of the proposed estimator is studied and comparisons are done with others. Depending on the simulation and real data results in the sense of mean squared error, the proposed estimator is superior to the other estimators.


[1] F. Akdeniz and E. A. Duran, Liu-type estimator in semiparametric regression models , J. Stat. Comput. Simul., 80(8)(2010) 853–871.
[2] A. M. Al-Abood and D. H. Young, Improved deviance goodness of fit statistics for a gamma regression model, Commun. Stat. Methods, 15(6)(1986) 1865–1874.
[3] Z. Y. Algamal, Developing a ridge estimator for the gamma regression model , J. Chemom., 32(10)(2018) e3054.
[4] Z. Algamal, Shrinkage estimators for gamma regression model , Electron. J. Appl. Stat. Anal., 11(1)(2018) 253–268,
[5] M. I. Alheety and B. M. Golam Kibria, Modified Liu-type estimator based on (r− k) class estimator, Commun. Stat. Methods, 42(2)(2013) 304–319.
[6] Y. Asar, Liu-type negative binomial regression: A comparison of recent estimators and applications, In: Trends Perspect. Linear Stat. Inference, Springer, 2018. pp. 23–39.
[7] Y. Asar and A. Gen¸c, New shrinkage parameters for the Liu-type logistic estimators, Commun. Stat. Comput., 45(3)(2016) 1094–1103.
[8] M. R. Baye and D. F. Parker, Combining ridge and principal component regression: a money demand illustration, Commun. Stat. Methods, 13(2)(1984) 197–205.
[9] P. De Jong and G. Z. Heller, Generalized linear models for insurance data, Cambridge Books, 2008.
[10] E. Dunder, S. Gumustekin, and M. A. Cengiz, Variable selection in gamma regression models via artificial bee colony algorithm, J. Appl. Stat., 45(1)(2018) 8–16.
[11] A. E. Hoerl and R. W. Kennard, Ridge regression: applications to nonorthogonal problems, Technometrics, 12(1)(1970) 69–82.
[12] D. Inan and B. E. Erdogan, Liu-type logistic estimator, Commun. Stat. Comput., 42(7)(2013) 1578–1586.
[13] S. Ka¸cıranlar and S. Sakallıo˘glu, Combining the Liu estimator and the principal component regression estimator, 2001.
[14] L. Kejian, A new class of blased estimate in linear regression, Commun. Stat. Methods, 22(2)(1993) 393–402.
[15] B. M. G. Kibria, Performance of some new ridge regression estimators, Commun. Stat. Comput., 32(2)(2003) 419–435.
[16] F. Kurto˘glu and M. R. Ozkale, Liu estimation in generalized linear models: application on gamma distributed response variable, Stat. Pap., 57(4)(2016) 911–928.
[17] M. J. Mackinnon and M. L. Puterman, Collinearity in generalized linear models, Commun. Stat. methods, 18(9)(1989) 3463–3472.
[18] K. M˚ansson, On ridge estimators for the negative binomial regression model, Econ. Model., 29(2)(2012) 178–184.
[19] K. Mansson, B. M. G. Kibria, P. Sjolander, and G. Shukur, Improved Liu estimators for the Poisson regression model, Int. J. Stat. Probab., 1(1)(2012) 2.
[20] K. M˚ansson and G. Shukur, A Poisson ridge regression estimator, Econ. Model., 28(4)(2011) 1475–1481.
[21] A. S. Malehi, F. Pourmotahari and K. A. Angali, Statistical models for the analysis of skewed healthcare cost data: a simulation study, Health Econ. Rev., 5(1)(2015) 1–16.
[22] G. Muniz and B. M. G. Kibria, On some ridge regression estimators: An empirical comparisons, Commun. Stat. Comput., 38(3)(2009) 621-630 .
[23] M. R. Ozkale and S. Kaciranlar, The restricted and unrestricted two-parameter estimators, Commun. Stat. Methods, 36(15)(2007) 2707–2725.
[24] B. Segerstedt, On ordinary ridge regression in generalized linear models, Commun. Stat. Methods, 21(8)(1992) 2227–2246.
[25] R. L. Schaefer, L. D. Roi, and R. A. Wolfe, A ridge logistic estimator, Commun. Stat. Methods, 13(1)(1984) 99–113.
[26] N. N. Urgan and M. Tez, Liu estimator in logistic regression when the data are collinear, In: 20th Euro Mini conf., 2008, pp. 323–327.
[27] M. Wasef Hattab, A derivation of prediction intervals for gamma regression, J. Stat. Comput. Simul., 86(17)(2016) 3512–3526.
[28] J. Wu and Y. Asar, More on the restricted Liu estimator in the logistic regression model, Commun. Stat. Comput., 46(5)(2017) 3680–3689.
[29] H. Yang and X. Chang, A new two-parameter estimator in linear regression, Commun. Stat. Methods, 39(6)(2010) 923–934.
Volume 13, Issue 1
March 2022
Pages 2455-2465
  • Receive Date: 20 May 2021
  • Revise Date: 28 August 2021
  • Accept Date: 12 October 2021