The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses

Atıf Abbası; Revan Özkale

doi:10.15672/hujms.715206

Araştırma Makalesi

Yıl 2021, Cilt: 50 Sayı: 2, 594 - 611, 11.04.2021

Atıf Abbası , Revan Özkale

https://doi.org/10.15672/hujms.715206

Cited By: 7

Öz

Kaynakça

[1] A. Agresti, An Introduction to Categorical Data Analysis, John Wiley and Sons, New Jersey, 2007.
[2] F.S.M. Batah, M.R. Özkale and S.D. Gore, Combining unbiased ridge and principal component regression estimators, Comm. Statist. Theory Methods 38 (13), 2201-2209, 2009.
[3] M.R. Baye and D.F. Parker, Combining ridge and principal component regression: A money demand illustration, Comm. Statist. Theory Methods 13 (2), 197-205, 1984.
[4] P.J. Green, Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives, J. Roy. Statist. Soc. Ser. B 46 (2), 149- 170, 1984.
[5] A.E. Hoerl and R.W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems, Tecnometrics 12 (1), 55-67, 1970.
[6] A.E. Hoerl, R.W. Kennard and K.F. Baldwin, Ridge regression: Some simulations, Comm. Statist. Theory Methods 4 (2), 105-123, 1975.
[7] D. Inan, Combining the Liu-type estimator and the principal component regression estimator, Statist. Papers 56 (1), 147-156, 2015.
[8] F. Kurtoğlu and M.R. Özkale, Liu estimation in generalized linear models: Application on gamma distributed response variable, Statist. Papers 57 (4), 911-928, 2016.
[9] F. Kurtoğlu and M.R. Özkale, Restricted ridge estimator in generalized linear models: Monte Carlo simulation studies on Poisson and binomial distributed responses, Comm. Statist. Simulation Comput. 48 (4), 1-28, 2017.
[10] F. Kurtoğlu and M.R. Özkale, Restricted Liu estimator in generalized linear models: Monte Carlo simulation studies on gamma and Poisson distributed responses, Hacet. J. Math. Stat. 48 (4), 1191-1218, 2019.
[11] M.J. Mackinnon and M.L. Puterman, Collinearity in generalized linear models, Comm. Statist. Theory Methods 18 (9), 3463-3472, 1989.
[12] K. Månsson, B.M.G. Kibria and G. Shukur, On Liu estimators for the logit regression model, Econ. Model. 29 (4), 1483-1488, 2012.
[13] K. Månsson and G. Shukur, A Poisson ridge regression estimator, Econ. Model. 28 (4), 1475-1481, 2011.
[14] B.D. Marx and E.P. Smith, Trust principal component estimation for generalized linear regression, Biometrika 77 (1), 23-31, 2019.
[15] G.C. McDonald and D.I. Galarneau, A Monte Carlo evaluation of some ridge-type estimators, J. Amer. Statist. Assoc. 70 (350), 407-416, 1975.
[16] J.A. Nelder and R.W.M. Wedderburn, Generalized linear models, J. Roy. Statist. Soc. Ser. A 135 (3), 370-384, 1972.
[17] H. Nyquist, Restricted estimation of generalized linear models, J. R. Stat. Soc. Ser. C. Appl. Stat. 40 (1), 133-141, 1991.
[18] M.R. Özkale, The r-d class estimator in generalized linear models: Applications on gamma, Poisson and binomial distributed responses, J. Stat. Comput. Simul. 89 (4), 615-640, 2019.
[19] M.R. Özkale, The red indicator and corrected VIFs in generalized linear models, Comm. Statist. Simulation Comput., Published Online, 2020.
[20] M.R. Özkale and E. Arıcan, A new biased estimator in logistic regression model, Statistics 50 (2), 233-253, 2016.
[21] M.R. Özkale and H. Nyquist, The stochastic restricted ridge estimator in generalized linear models, Statist. Papers, Published Online, 2019, DOI:https://doi.org/10.1007/s00362-019-01142-7.
[22] M. Qasim, B.M.G. Kibria, K. Månsson and P. Sjölander, A new Poisson Liu Regression Estimator: Method and application J. Appl. Stat., Published Online, 2019, DOI:10.1080/02664763.2019.1707485
[23] B. Segerstedt, On ordinary ridge regression in generalized linear models, Comm. Statist. Theory Methods 21 (8), 2227-2246, 1992.
[24] E.P. Smith and B.D. Marx, Ill-conditioned information matrices, generalized linear models and estimation of the effects of acid rain, Environmetrics 1 (1), 57-71, 1990.
[25] S. Türkan and G. Özel, A new modified Jackknifed estimator for the Poisson regression model, J. Appl. Stat. 43 (10), 1892-1905, 2016.
[26] N. Varathan and P. Wijekoon, Optimal stochastic restricted logistic estimator, Statist. Papers doi: 10.1007/s00362-019-01121-y, 2019.
[27] L.A. Weissfeld and S.M. Sereika, A multicollinearity diagnostic for generalized linear models, Comm. Statist. Theory Methods 20 (4), 1183-1198, 1991.
[28] J. Wu and Y. Asar, On almost unbiased ridge logistic estimator for the logistic regression model, Hacet. J. Math. Stat. 45 (3), 989-998, 2016.
[29] J. Wu and H. Yang, On the principal component Liu-type estimator in linear regression, Comm. Statist. Simulation Comput. 44 (8), 2061-2072, 2015.

The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses

Yıl 2021, Cilt: 50 Sayı: 2, 594 - 611, 11.04.2021

Atıf Abbası , Revan Özkale

https://doi.org/10.15672/hujms.715206

Cited By: 7

Öz

Multicollinearity is considered to be a significant problem in the estimation of parameters not only in general linear models, but also in generalized linear models (GLMs). Thus, in order to alleviate the serious effects of multicollinearity a new estimator is proposed by combining the ridge and PCR estimators in GLMs. This new estimator is called the r-k class estimator in GLMs. The various comparisons of the new estimator are made with already existing estimators in the literature, which are maximum likelihood (ML) estimator, ridge and PCR estimators, respectively. The comparisons are to be made in terms of scalar MSE criterion. So that, a numerical example and application through simulation are mentioned in the study for Poisson and Gamma response variables, respectively. On the basis of results it is found that, the proposed estimator outperforms all of its competitors comprehensively.

Anahtar Kelimeler

maximum likelihood estimator, principal component regression, ridge estimator, r-k class estimator, reduction rate, Gamma, Poisson data

Kaynakça

[1] A. Agresti, An Introduction to Categorical Data Analysis, John Wiley and Sons, New Jersey, 2007.
[2] F.S.M. Batah, M.R. Özkale and S.D. Gore, Combining unbiased ridge and principal component regression estimators, Comm. Statist. Theory Methods 38 (13), 2201-2209, 2009.
[3] M.R. Baye and D.F. Parker, Combining ridge and principal component regression: A money demand illustration, Comm. Statist. Theory Methods 13 (2), 197-205, 1984.
[4] P.J. Green, Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives, J. Roy. Statist. Soc. Ser. B 46 (2), 149- 170, 1984.
[5] A.E. Hoerl and R.W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems, Tecnometrics 12 (1), 55-67, 1970.
[6] A.E. Hoerl, R.W. Kennard and K.F. Baldwin, Ridge regression: Some simulations, Comm. Statist. Theory Methods 4 (2), 105-123, 1975.
[7] D. Inan, Combining the Liu-type estimator and the principal component regression estimator, Statist. Papers 56 (1), 147-156, 2015.
[8] F. Kurtoğlu and M.R. Özkale, Liu estimation in generalized linear models: Application on gamma distributed response variable, Statist. Papers 57 (4), 911-928, 2016.
[9] F. Kurtoğlu and M.R. Özkale, Restricted ridge estimator in generalized linear models: Monte Carlo simulation studies on Poisson and binomial distributed responses, Comm. Statist. Simulation Comput. 48 (4), 1-28, 2017.
[10] F. Kurtoğlu and M.R. Özkale, Restricted Liu estimator in generalized linear models: Monte Carlo simulation studies on gamma and Poisson distributed responses, Hacet. J. Math. Stat. 48 (4), 1191-1218, 2019.
[11] M.J. Mackinnon and M.L. Puterman, Collinearity in generalized linear models, Comm. Statist. Theory Methods 18 (9), 3463-3472, 1989.
[12] K. Månsson, B.M.G. Kibria and G. Shukur, On Liu estimators for the logit regression model, Econ. Model. 29 (4), 1483-1488, 2012.
[13] K. Månsson and G. Shukur, A Poisson ridge regression estimator, Econ. Model. 28 (4), 1475-1481, 2011.
[14] B.D. Marx and E.P. Smith, Trust principal component estimation for generalized linear regression, Biometrika 77 (1), 23-31, 2019.
[15] G.C. McDonald and D.I. Galarneau, A Monte Carlo evaluation of some ridge-type estimators, J. Amer. Statist. Assoc. 70 (350), 407-416, 1975.
[16] J.A. Nelder and R.W.M. Wedderburn, Generalized linear models, J. Roy. Statist. Soc. Ser. A 135 (3), 370-384, 1972.
[17] H. Nyquist, Restricted estimation of generalized linear models, J. R. Stat. Soc. Ser. C. Appl. Stat. 40 (1), 133-141, 1991.
[18] M.R. Özkale, The r-d class estimator in generalized linear models: Applications on gamma, Poisson and binomial distributed responses, J. Stat. Comput. Simul. 89 (4), 615-640, 2019.
[19] M.R. Özkale, The red indicator and corrected VIFs in generalized linear models, Comm. Statist. Simulation Comput., Published Online, 2020.
[20] M.R. Özkale and E. Arıcan, A new biased estimator in logistic regression model, Statistics 50 (2), 233-253, 2016.
[21] M.R. Özkale and H. Nyquist, The stochastic restricted ridge estimator in generalized linear models, Statist. Papers, Published Online, 2019, DOI:https://doi.org/10.1007/s00362-019-01142-7.
[22] M. Qasim, B.M.G. Kibria, K. Månsson and P. Sjölander, A new Poisson Liu Regression Estimator: Method and application J. Appl. Stat., Published Online, 2019, DOI:10.1080/02664763.2019.1707485
[23] B. Segerstedt, On ordinary ridge regression in generalized linear models, Comm. Statist. Theory Methods 21 (8), 2227-2246, 1992.
[24] E.P. Smith and B.D. Marx, Ill-conditioned information matrices, generalized linear models and estimation of the effects of acid rain, Environmetrics 1 (1), 57-71, 1990.
[25] S. Türkan and G. Özel, A new modified Jackknifed estimator for the Poisson regression model, J. Appl. Stat. 43 (10), 1892-1905, 2016.
[26] N. Varathan and P. Wijekoon, Optimal stochastic restricted logistic estimator, Statist. Papers doi: 10.1007/s00362-019-01121-y, 2019.
[27] L.A. Weissfeld and S.M. Sereika, A multicollinearity diagnostic for generalized linear models, Comm. Statist. Theory Methods 20 (4), 1183-1198, 1991.
[28] J. Wu and Y. Asar, On almost unbiased ridge logistic estimator for the logistic regression model, Hacet. J. Math. Stat. 45 (3), 989-998, 2016.
[29] J. Wu and H. Yang, On the principal component Liu-type estimator in linear regression, Comm. Statist. Simulation Comput. 44 (8), 2061-2072, 2015.

Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	İstatistik
Bölüm	İstatistik
Yazarlar	Atıf Abbası 0000-0001-9987-0193 Revan Özkale 0000-0001-7085-7403
Yayımlanma Tarihi	11 Nisan 2021
Yayımlandığı Sayı	Yıl 2021 Cilt: 50 Sayı: 2

Kaynak Göster

APA	Abbası, A., & Özkale, R. (2021). The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses. Hacettepe Journal of Mathematics and Statistics, 50(2), 594-611. https://doi.org/10.15672/hujms.715206
AMA	Abbası A, Özkale R. The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses. Hacettepe Journal of Mathematics and Statistics. Nisan 2021;50(2):594-611. doi:10.15672/hujms.715206
Chicago	Abbası, Atıf, ve Revan Özkale. “The R-K Class Estimator in Generalized Linear Models Applicable With Simulation and Empirical Study Using a Poisson and Gamma Responses”. Hacettepe Journal of Mathematics and Statistics 50, sy. 2 (Nisan 2021): 594-611. https://doi.org/10.15672/hujms.715206.
EndNote	Abbası A, Özkale R (01 Nisan 2021) The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses. Hacettepe Journal of Mathematics and Statistics 50 2 594–611.
IEEE	A. Abbası ve R. Özkale, “The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, ss. 594–611, 2021, doi: 10.15672/hujms.715206.
ISNAD	Abbası, Atıf - Özkale, Revan. “The R-K Class Estimator in Generalized Linear Models Applicable With Simulation and Empirical Study Using a Poisson and Gamma Responses”. Hacettepe Journal of Mathematics and Statistics 50/2 (Nisan 2021), 594-611. https://doi.org/10.15672/hujms.715206.
JAMA	Abbası A, Özkale R. The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses. Hacettepe Journal of Mathematics and Statistics. 2021;50:594–611.
MLA	Abbası, Atıf ve Revan Özkale. “The R-K Class Estimator in Generalized Linear Models Applicable With Simulation and Empirical Study Using a Poisson and Gamma Responses”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, 2021, ss. 594-11, doi:10.15672/hujms.715206.
Vancouver	Abbası A, Özkale R. The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses. Hacettepe Journal of Mathematics and Statistics. 2021;50(2):594-611.