International Journal of Nonlinear Analysis and Applications
Jackknifing K-L estimator in generalized linear models
Document Type : Research Paper
Authors
1 Department of Economics, College of Administration and Economics, University of Anbar, Anbar, Iraq
2 Department of Statistics and Informatics, University of Mosul, Mosul, Iraq
Abstract
It is a challenge in the real application when modelling the relationship between the response variable and several explanatory variables when the existence of collinearity. Traditionally, in order to avoid this issue, several shrinkage estimators are proposed. Among them is the Kibria and Lukman estimator (K-L). In this study, a jackknifed version of the K-L estimator is proposed in the generalized linear model that combines the Jackknife procedure with the K-L estimator to reduce the biasedness. Our Monte Carlo simulation results and the real data application related to the inverse Gaussian regression model suggest that the proposed estimator can bring significant improvement relative to other competitor estimators, in terms of absolute bias and mean squared error.
Keywords
[1] E. Akdeniz Duran and F. Akdeniz, Efficiency of the modified jackknifed Liu-type estimator, Statist. Papers 53(2)
(2012) 265–280.
[2] M.N. Akram, M. Amin and M. Amanullah, Two-parameter estimator for the inverse Gaussian regression model,
Commun. Statist. Simul. Comput. 2020 (2020) 1–19.
[3] A. Alkhateeb and Z. Algamal, Jackknifed liu-type estimator in poisson regression model, J. Iran. Statist. Soc.
19(1) (2020) 21–37.
[4] Z.Y. Algamal, Developing a ridge estimator for the gamma regression model, J. Chemometrics 32(10) (2018).
[5] Z.Y. Algamal, A new method for choosing the biasing parameter in ridge estimator for generalized linear model,
Chemometrics Intell. Lab. Syst. 183 (2018) 96–101.
[6] Z.Y. Algamal, Performance of ridge estimator in inverse Gaussian regression model, Commun. Statist. Theory
Methods 48(15) (2018) 3836–3849.
[7] Z.Y. Algamal, Shrinkage estimators for gamma regression model, Electron. J. Appl. Statist. Anal. 11(1) (2018)
253–268.
[8] Z.Y. Algamal, Shrinkage parameter selection via modified cross-validation approach for ridge regression model,
Commun. Statist. 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.
Pract. Exper. 2021 (2021).
[10] Z.Y. Algamal, Performance of ridge estimator in inverse Gaussian regression model, Commun. Statist. Theory
Methods 48(15) (2018) 3836–3849.
[11] Z.Y. Algamal and M.M. Alanaz, Proposed methods in estimating the ridge regression parameter in Poisson regression model, Electron. J. Appl. Statist. Anal. 11(2) (2018) 506–15.
[12] Z.Y. Algamal and Y. Asar, Liu-type estimator for the gamma regression model, Commun. Statist. Simul. Comput.
49(8) (2018) 2035–2048.
[13] Z. Algamal, Shrinkage estimators for gamma regression model, Electron. J. Appl. Statist. Anal. 11(1) (2018)
253–268.
[14] Z. Algamal, Generalized ridge estimator shrinkage estimation based on particle swarm optimization algorithm,
Iraqi J. Statist. Sci. 17(32) (2020) 37–52.
[15] Y. Al-Taweel, Z. 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.
[16] J. Correa-Basurto, C. Flores-Sandoval, J. Mar´ın-Cruz, A. Rojo-Dom´ınguez, L.M. Espinoza-Fonseca and J.G.J.
Trujillo-Ferrara, Docking and quantum mechanic studies on cholinesterases and their inhibitors, Eur. J. Medicinal
Chem. 42(1) (2007) 10–19.
[17] R. Farebrother, Further results on the mean square error of ridge regression, J. Royal Statist. Soc. Ser. B 38(3)
(1976) 248–250.
[18] M.H. Gruber, The efficiency of jack-knifed and usual ridge type estimators: A comparison, Statist. Probab. Lett.
11(1) (1991) 49–51.
[19] D.V. Hinkley, Jackknifing in unbalanced situations, Technometrics 19(3) (1977) 285–292.
[20] A.E. Hoerl and R.W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems, Technometrics
12(1) (1970) 55–67.
[21] A.E. Hoerl, R.W. Kannard and K.F. Baldwin, Ridge regression: Some simulations, Comm. Statist. Theory
Methods 4(2) (1975) 105–123.
[22] B.M.G. Kibria, Performance of some new ridge regression estimators, Commun. Statist. Simul. Comput. 32(2)
(2003) 419–435.
[23] B.M.G. Kibria and A.F. Lukman, A new ridge-type estimator for the linear regression model: simulations and
applications, Scientifica 2020 (2020).
[24] G. Kibria, K. M˚ansson and G. Shukur, Performance of some logistic ridge regression estimators, Comput. Econ.
40(4) (2012) 401–414.
[25] M. Khurana, Y.P. Chaubey and S. Chandra, Jackknifing the ridge regression estimator: A revisit, Comm. Statist.
Theory Methods 43(24) (2014) 5249–5262.
[26] F. Kurto˘glu and M.R. Ozkale, ¨ Liu estimation in generalized linear models: application on gamma distributed
response variable, Statist. Papers 57(4) (2016) 911–928.[27] K. Liu, A new class of biased estimate in linear regression, Comm. Statist. Theory Methods 22 (1993) 393–402.
[28] G. Liu and S. Piantadosi, Ridge estimation in generalized linear models and proportional hazards regressions,
Comm. Statist. Theory Methods. 46(23) (2016) 11466–11479.
[29] A.F. Lukman, Z.Y. Algamal, B.M.G. Kibria and K. Ayinde, The KL estimator for the inverse Gaussian regression
model, Concurr. Comput. Pract. Exper. 33(13) (2021).
[30] 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, Scientifica 2021 (2021).
[31] M.J. Mackinnon and M.L. Puterman, Collinearity in generalized linear models, Commun. Statist. Theory Methods. 18(9) (1989) 3463–3472.
[32] K. M˚ansson and G. Shukur, A Poisson ridge regression estimator, Economic Modell. 28(4) (2011) 1475–1481.
[33] P. McCullagh, J.A. Nelder and P. McCullagh, Generalized Linear Models, 2nd ed. New York: Chapman and Hall
London, 1989.
[34] H.S. Mohammed and Z.Y. Algamal, Shrinkage estimators for semiparametric regression model, J. Phys. Conf.
Ser. 1897(1) (2021).
[35] F. Noeel and Z.Y. Algamal, Almost unbiased ridge estimator in the count data regression models, Electron. J.
Appl. Statist. Anal. 14(1) (2021) 44–57.
[36] H. Nyquist, Applications of the jackknife procedure in ridge regression, Comput. Statist. Data Anal. 6(2) (1988)
177–183.
[37] H. Nyquist, Restricted estimation of generalized linear models, J. Royal Statist. Soc. Ser. C 40(1) (1991) 133–141.
[38] 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.
[39] 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).
[40] B. Segerstedt, On ordinary ridge regression in generalized linear models, Commun. Statist. Theory Methods.
21(8) (1992) 2227–2246.
[41] M.R. Ozkale and E. Arıcan, ¨ A first-order approximated jackknifed ridge estimator in binary logistic regression,
Comput. Statist. 34(2) (2018) 683–712.
[42] R. Shamany, N.N. Alobaidi and Z.Y. Algamal, A new two-parameter estimator for the inverse Gaussian regression
model with application in chemometrics, Electron. J. Appl. Statist. Anal. 12(2) (2019) 453–464.
[43] B. Singh, Y. Chaubey and T. Dwivedi, An almost unbiased ridge estimator, Indian J. Statist. Ser. B. 13 (1986)
342–346.
[44] S. T¨urkan and G. Ozel, ¨ A new modified Jackknifed estimator for the Poisson regression model, J. Appl. Statist.
43(10) (2015) 1892–1905.
[45] N. Yıldız, On the performance of the Jackknifed Liu-type estimator in linear regression model, Commun. Statist.
Theory Methods 47(9) (2018) 2278–2290.
(2012) 265–280.
[2] M.N. Akram, M. Amin and M. Amanullah, Two-parameter estimator for the inverse Gaussian regression model,
Commun. Statist. Simul. Comput. 2020 (2020) 1–19.
[3] A. Alkhateeb and Z. Algamal, Jackknifed liu-type estimator in poisson regression model, J. Iran. Statist. Soc.
19(1) (2020) 21–37.
[4] Z.Y. Algamal, Developing a ridge estimator for the gamma regression model, J. Chemometrics 32(10) (2018).
[5] Z.Y. Algamal, A new method for choosing the biasing parameter in ridge estimator for generalized linear model,
Chemometrics Intell. Lab. Syst. 183 (2018) 96–101.
[6] Z.Y. Algamal, Performance of ridge estimator in inverse Gaussian regression model, Commun. Statist. Theory
Methods 48(15) (2018) 3836–3849.
[7] Z.Y. Algamal, Shrinkage estimators for gamma regression model, Electron. J. Appl. Statist. Anal. 11(1) (2018)
253–268.
[8] Z.Y. Algamal, Shrinkage parameter selection via modified cross-validation approach for ridge regression model,
Commun. Statist. 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.
Pract. Exper. 2021 (2021).
[10] Z.Y. Algamal, Performance of ridge estimator in inverse Gaussian regression model, Commun. Statist. Theory
Methods 48(15) (2018) 3836–3849.
[11] Z.Y. Algamal and M.M. Alanaz, Proposed methods in estimating the ridge regression parameter in Poisson regression model, Electron. J. Appl. Statist. Anal. 11(2) (2018) 506–15.
[12] Z.Y. Algamal and Y. Asar, Liu-type estimator for the gamma regression model, Commun. Statist. Simul. Comput.
49(8) (2018) 2035–2048.
[13] Z. Algamal, Shrinkage estimators for gamma regression model, Electron. J. Appl. Statist. Anal. 11(1) (2018)
253–268.
[14] Z. Algamal, Generalized ridge estimator shrinkage estimation based on particle swarm optimization algorithm,
Iraqi J. Statist. Sci. 17(32) (2020) 37–52.
[15] Y. Al-Taweel, Z. 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.
[16] J. Correa-Basurto, C. Flores-Sandoval, J. Mar´ın-Cruz, A. Rojo-Dom´ınguez, L.M. Espinoza-Fonseca and J.G.J.
Trujillo-Ferrara, Docking and quantum mechanic studies on cholinesterases and their inhibitors, Eur. J. Medicinal
Chem. 42(1) (2007) 10–19.
[17] R. Farebrother, Further results on the mean square error of ridge regression, J. Royal Statist. Soc. Ser. B 38(3)
(1976) 248–250.
[18] M.H. Gruber, The efficiency of jack-knifed and usual ridge type estimators: A comparison, Statist. Probab. Lett.
11(1) (1991) 49–51.
[19] D.V. Hinkley, Jackknifing in unbalanced situations, Technometrics 19(3) (1977) 285–292.
[20] A.E. Hoerl and R.W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems, Technometrics
12(1) (1970) 55–67.
[21] A.E. Hoerl, R.W. Kannard and K.F. Baldwin, Ridge regression: Some simulations, Comm. Statist. Theory
Methods 4(2) (1975) 105–123.
[22] B.M.G. Kibria, Performance of some new ridge regression estimators, Commun. Statist. Simul. Comput. 32(2)
(2003) 419–435.
[23] B.M.G. Kibria and A.F. Lukman, A new ridge-type estimator for the linear regression model: simulations and
applications, Scientifica 2020 (2020).
[24] G. Kibria, K. M˚ansson and G. Shukur, Performance of some logistic ridge regression estimators, Comput. Econ.
40(4) (2012) 401–414.
[25] M. Khurana, Y.P. Chaubey and S. Chandra, Jackknifing the ridge regression estimator: A revisit, Comm. Statist.
Theory Methods 43(24) (2014) 5249–5262.
[26] F. Kurto˘glu and M.R. Ozkale, ¨ Liu estimation in generalized linear models: application on gamma distributed
response variable, Statist. Papers 57(4) (2016) 911–928.[27] K. Liu, A new class of biased estimate in linear regression, Comm. Statist. Theory Methods 22 (1993) 393–402.
[28] G. Liu and S. Piantadosi, Ridge estimation in generalized linear models and proportional hazards regressions,
Comm. Statist. Theory Methods. 46(23) (2016) 11466–11479.
[29] A.F. Lukman, Z.Y. Algamal, B.M.G. Kibria and K. Ayinde, The KL estimator for the inverse Gaussian regression
model, Concurr. Comput. Pract. Exper. 33(13) (2021).
[30] 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, Scientifica 2021 (2021).
[31] M.J. Mackinnon and M.L. Puterman, Collinearity in generalized linear models, Commun. Statist. Theory Methods. 18(9) (1989) 3463–3472.
[32] K. M˚ansson and G. Shukur, A Poisson ridge regression estimator, Economic Modell. 28(4) (2011) 1475–1481.
[33] P. McCullagh, J.A. Nelder and P. McCullagh, Generalized Linear Models, 2nd ed. New York: Chapman and Hall
London, 1989.
[34] H.S. Mohammed and Z.Y. Algamal, Shrinkage estimators for semiparametric regression model, J. Phys. Conf.
Ser. 1897(1) (2021).
[35] F. Noeel and Z.Y. Algamal, Almost unbiased ridge estimator in the count data regression models, Electron. J.
Appl. Statist. Anal. 14(1) (2021) 44–57.
[36] H. Nyquist, Applications of the jackknife procedure in ridge regression, Comput. Statist. Data Anal. 6(2) (1988)
177–183.
[37] H. Nyquist, Restricted estimation of generalized linear models, J. Royal Statist. Soc. Ser. C 40(1) (1991) 133–141.
[38] 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.
[39] 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).
[40] B. Segerstedt, On ordinary ridge regression in generalized linear models, Commun. Statist. Theory Methods.
21(8) (1992) 2227–2246.
[41] M.R. Ozkale and E. Arıcan, ¨ A first-order approximated jackknifed ridge estimator in binary logistic regression,
Comput. Statist. 34(2) (2018) 683–712.
[42] R. Shamany, N.N. Alobaidi and Z.Y. Algamal, A new two-parameter estimator for the inverse Gaussian regression
model with application in chemometrics, Electron. J. Appl. Statist. Anal. 12(2) (2019) 453–464.
[43] B. Singh, Y. Chaubey and T. Dwivedi, An almost unbiased ridge estimator, Indian J. Statist. Ser. B. 13 (1986)
342–346.
[44] S. T¨urkan and G. Ozel, ¨ A new modified Jackknifed estimator for the Poisson regression model, J. Appl. Statist.
43(10) (2015) 1892–1905.
[45] N. Yıldız, On the performance of the Jackknifed Liu-type estimator in linear regression model, Commun. Statist.
Theory Methods 47(9) (2018) 2278–2290.
)
Volume 12, Special Issue
December 2021Pages 2093-2104
- Receive Date: 02 October 2022
- Revise Date: 12 November 2022
- Accept Date: 04 December 2022