International Journal of Nonlinear Analysis and Applications
Jackknifed Liu-type estimator in the negative binomial regression model
Document Type : Research Paper
Authors
1 Northern Technical University, Mosul, Iraq
2 Department of Management Information Systems, University of Mosul, Mosul, Iraq
3 Department of Statistics and Informatics, College of Computer science and Mathematics, University of Mosul, Mosul, Iraq
Abstract
The Liu estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of Inter-correlated (multicollinearity). The negative binomial regression model is a well-known model in the application when the response variable is non-negative integers or counts. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator of the negative binomial coefficients. To overcome this problem, a negative binomial Liu estimator has been proposed by numerous researchers. In this paper, a Jackknifed Liu-type negative binomial estimator (JNBLTE) is proposed and derived. The idea behind the JNBLTE is to decrease the shrinkage parameter and, therefore, the resultant estimator can be better with a small amount of bias. Our Monte Carlo simulation results suggest that the JNBLTE estimator can bring significant improvement relative to other existing estimators. In addition, the real application results demonstrate that the JNBLTE estimator outperforms both the negative binomial Liu estimator and maximum likelihood estimators in terms of predictive performance.
Keywords
optimization algorithm, Elect. J. Appl. Stat. Anal. 14(1) (2021) 254–265.
[2] E. Akdeniz Duran and F. Akdeniz, Efficiency of the modified jackknifed Liu-type estimator, Stat. Papers 53(2)
(2012) 265–280.
[3] Y. Al-Taweel, Z.J. Algamal and N. Sciences, Some almost unbiased ridge regression estimators for the zero-inflated
negative binomial regression model, Period. Engin. Natural Sci. 8(1) (2020) 248–255.
[4] Z.Y. Algamal, Diagnostic in poisson regression models, Elect. J. Appl. Stat. Anal. 5(2) (2012) 178–186.
[5] Z.Y. Algamal, Biased estimators in Poisson regression model in the presence of multicollinearity: A subject review,
Al-Qadisiyah J. Administ. Economic Sci. 20(1) (2018) 37–43.
[6] Z.Y. Algamal, Developing a ridge estimator for the gamma regression model, J. Chemomet. 32(10) (2018).
[7] Z.Y. Algamal, A new method for choosing the biasing parameter in ridge estimator for generalized linear model,
Chemomet. Intel. Laboratory Syst. 183 (2018) 96–101.[8] Z.Y. Algamal, Shrinkage parameter selection via modified cross-validation approach for ridge regression model,
Commun. Stat. Simul. Comput. 49(7) (2018) 1922–1930.
[9] Z.Y. Algamal and M.R. Abonazel, Developing a Liu-type estimator in beta regression model, Concur. Comput.
Practice Exper. (2021) e6685.
[10] Z.Y. Algamal, and M.M. Alanaz, Proposed methods in estimating the ridge regression parameter in Poisson
regression model, Elect. J. Appl. Stat. Anal. 11(2) (2018) 506–515.
[11] Z.Y. Algamal and Y. Asar, Liu-type estimator for the gamma regression model, Commun. Stat. Simul. Comput.
49(8) (2018) 2035–2048.
[12] Z.Y. Algamal, Shrinkage estimators for gamma regression model, Elect. J. Appl. Stat. Anal. 11(1) (2018) 253–268.
[13] Z.Y. Algamal, Generalized ridge estimator shrinkage estimation based on particle swarm optimization algorithm,
Iraqi J. Stat. Sci. 17(32) (2020) 37–52.
[14] A. Alkhateeb and Z.Y. Algamal, Jackknifed Liu-type estimator in Poisson regression model, J. Iran. Stat. Soc.
19(1) (2020) 21–37.
[15] N.N. Alobaidi, R.E. Shamany and Z.Y. Algamal, A New Ridge Estimator for the Negative Binomial Regression
Model, Thai. Stat. 19(1) (2021) 116–125.
[16] Y. Asar and A. Gen¸c, A new two-parameter estimator for the Poisson regression model, Iran. J. Sci. Technol.
Trans. A Sci. 42(2) (2017) 793–803.
[17] F.S.M. Batah, T.V. Ramanathan and S.D. Gore, The Efficiency of Modified Jackknife and Ridge Type Regression
Estimators: A Comparison, Surveys in Mathematics & its Applications, 2008.
[18] A.C. Cameron and P.K. Trivedi, Regression Analysis of Count Data, Cambridge university press, 2013.
[19] P. De Jong and G.Z. Heller, Generalized Linear Models for Insurance Data, Cambridge University Press Cambridge, 2008.
[20] D.V. Hinkley, Jackknifing in unbalanced situations, Technomet. 19(3) (1977) 285–292.
[21] A.E. Hoerl and R.W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems, Technomet.
12(1) (1970) 55–67.
[22] M. Kandemir C¸ etinkaya and S. Ka¸cıranlar, Improved two-parameter estimators for the negative binomial and
Poisson regression models, J. Stat. Comput. Simul. 89(14) (2019) 2645–2660.
[23] B.G. Kibria, K. M˚ansson and G. Shukur, A simulation study of some biasing parameters for the ridge type
estimation of Poisson regression, Commun. Stat. Simul. Comput. 44(4) (2015) 943–957.
[24] B.M.G. Kibria, Performance of some new ridge regression estimators, Commun. Stat. Simul. Comput. 32(2)
(2003) 419–435.
[25] B.M.G. Kibria, K. M˚ansson and G. Shukur, A simulation study of some biasing parameters for the Ridge Type
estimation of Poisson regression, Commun. Stat. Theory Meth. 44(4) (2015) 943–957.
[26] K. Liu, A new class of blased estimate in linear regression, Commun. Stat. Theory Meth. 22(2) (1993) 393–402.
[27] K. Liu, Using Liu-type estimator to combat collinearity, Commun. Stat. Theory Meth. 32(5) (2003) 1009–1020.
[28] A.F. Lukman, Z.Y. Algamal, B.M.G. Kibria and K. Ayinde, The KL estimator for the inverse Gaussian regression
model, Concur. Comput. Practice Exper. 33(13) (2021).
[29] A.F. Lukman, I. Dawoud, B.M.G. Kibria, Z.Y. Algamal and B. Aladeitan, A new Ridge-Type estimator for the
Gamma regression model, Scientif. (Cairo) 2021 5545356.
[30] K. M˚ansson, On ridge estimators for the negative binomial regression model, Economic Model. 29(2) (2012)
178–184.
[31] K. M˚ansson, Developing a Liu estimator for the negative binomial regression model: method and application, J.
Stat. Comput. Simul. 83(9) (2013) 1773–1780.
[32] K. Mansson, B.G. Kibria, P. Sjolander and G. Shukur, Improved Liu estimators for the Poisson regression model,
Int. J. Stat. Probab. 1(1) (2012) 2.
[33] K. M˚ansson and G. Shukur, A Poisson ridge regression estimator, Economic Model. 28(4) (2011) 1475–1481.
[34] H.S. Mohammed and Z.Y. Algamal, Shrinkage estimators for semiparametric regression model, J. Phys. Conf.
Ser. 1897(1) (2021).
[35] H. Nyquist, Applications of the jackknife procedure in ridge regression, Comput. Stat. Data Anal. 6(2) (1988)
177–183.
[36] M.H. Quenouille, Notes on bias in estimation, Biomet. 43(3/4) (1956) 353–360.
[37] 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) (2019) 2921–2928.
[38] N.K. Rashad, N.M. Hammood and Z.Y. Algamal, Generalized ridge estimator in negative binomial regression
model, J. Phys. Conf. Ser. 1897(1) (2021).
[39] R. Shamany, N.M. Alobaidi and Z.Y. Algamal, A new two-parameter estimator for the inverse Gaussian regressionmodel with application in chemometrics, Elect. J. Appl. Stat. Anal. 12(2) (2019) 453–464.
[40] B. Singh, Y. Chaubey and T. Dwivedi, An almost unbiased ridge estimator, Indian J. Stat. Ser. B 48(3) (1986)
342–346.
[41] J. Tukey, Bias and confidence in not quite large samples, Ann. Math. Statist. 29 (1958) 614.
[42] S. T¨urkan and G. Ozel, ¨ A new modified Jackknifed estimator for the Poisson regression model, J. Appl. Stat.
43(10) (2015) 1892–1905.
[43] S. T¨urkan and G. Ozel, ¨ A Jackknifed estimators for the Negative Binomial regression model, Commun. Stat.
Simul. Comput. 47(6) (2018) 1845–1865.
[44] A. Z. Yahya, Performance of ridge estimator in inverse Gaussian regression model, Commun. Stat. Theory Meth.
48(15) (2018) 3836–3849.
[45] Yıldız, On the performance of the Jackknifed Liu-type estimator in linear regression model, Commun. Stat. Theory
Meth. 47(9) (2017) 2278–2290.
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Volume 13, Issue 1
March 2022Pages 2675-2684
- Receive Date: 16 September 2021
- Revise Date: 21 October 2021
- Accept Date: 12 December 2021