KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 2

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

Atif Abbasi
M. Revan Özkale
Sayfa
594–611
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

On the basis of results it is found that, the proposed estimator outperforms all of its competitors comprehensively.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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).
📊
Temel Bulgular & Veri:Thus, in order to alleviate the serious effects of multicollinearity a new estimator is proposed by combining the ridge and PCR estimators in GLMs.
💡
Sonuç & Katkı:On the basis of results it is found that, the proposed estimator outperforms all of its competitors comprehensively.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:maximum likelihood estimator · principal component regression · ridge estimator

Abstract

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.

🔖

Bu Makaleye Atıf Yap

Abbasi, A., Özkale, M. R. (2022). 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, Cilt: 50 - Sayı: 2, 594–611. https://ajindex.com/articles/529486

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  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. A