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

Özkale, M.Revan; ABBASI, ATIF

doi:10.15672/hujms.715206

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

Atıf ABBASI, (The University of Azad Jammu and Kashmir Muzaffarabad, Department of Statistics, 13100, AJK, Pakistan)

Revan ÖZKALE (Çukurova Üniversitesi, Fen Edebiyat Fakültesi, İstatistik Bölümü, Adana, Türkiye)

Hacettepe Journal of Mathematics and Statistics

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Yıl: 2021 Cilt: 50 Sayı: 2 Sayfa Aralığı: 594 - 611 Metin Dili: İngilizce DOI: 10.15672/hujms.715206 İndeks Tarihi: 29-07-2022

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

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

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	ABBASI A, Özkale M (2021). The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses. , 594 - 611. 10.15672/hujms.715206
Chicago	ABBASI ATIF,Özkale M.Revan The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses. (2021): 594 - 611. 10.15672/hujms.715206
MLA	ABBASI ATIF,Özkale M.Revan The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses. , 2021, ss.594 - 611. 10.15672/hujms.715206
AMA	ABBASI A,Özkale M The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses. . 2021; 594 - 611. 10.15672/hujms.715206
Vancouver	ABBASI A,Özkale M The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses. . 2021; 594 - 611. 10.15672/hujms.715206
IEEE	ABBASI A,Özkale M "The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses." , ss.594 - 611, 2021. 10.15672/hujms.715206
ISNAD	ABBASI, ATIF - Özkale, M.Revan. "The r-k class estimator in generalized linear models applicable with simulation and empirical study using a Poisson and Gamma responses". (2021), 594-611. https://doi.org/10.15672/hujms.715206

APA	ABBASI A, Özkale M (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. 10.15672/hujms.715206
Chicago	ABBASI ATIF,Özkale M.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, no.2 (2021): 594 - 611. 10.15672/hujms.715206
MLA	ABBASI ATIF,Özkale M.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, vol.50, no.2, 2021, ss.594 - 611. 10.15672/hujms.715206
AMA	ABBASI A,Özkale M 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. 10.15672/hujms.715206
Vancouver	ABBASI A,Özkale M 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. 10.15672/hujms.715206
IEEE	ABBASI A,Özkale M "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, ss.594 - 611, 2021. 10.15672/hujms.715206
ISNAD	ABBASI, ATIF - Özkale, M.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 (2021), 594-611. https://doi.org/10.15672/hujms.715206