SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 4

Restricted Liu estimator in generalized linear models: Monte Carlo simulation studies on gamma and Poisson distributed responses

M. Revan Özkale
Fikriye Kurtoğlu
Pages
1250–1276
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results are illustrated by conducting simulation studies and numerical examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we introduce iterative restricted Liu estimator to combat multicollinearity in generalized linear models.
📊
Key Findings & Data:We also obtain necessary and sufficient conditions for the superiority of the first-order approximated restricted Liu estimator over the first-order approximated maximum likelihood and Liu estimators by the approximated mean squared error criterion.
💡
Conclusion & Impact:The results are illustrated by conducting simulation studies and numerical examples.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Restricted Liu estimation · Multicollinearity · Generalized linear models

Abstract

In this study, we introduce iterative restricted Liu estimator to combat multicollinearity in generalized linear models. We also obtain necessary and sufficient conditions for the superiority of the first-order approximated restricted Liu estimator over the first-order approximated maximum likelihood and Liu estimators by the approximated mean squared error criterion. The results are illustrated by conducting simulation studies and numerical examples.

🔖

Cite This Article

Özkale, M. R., Kurtoğlu, F. (2022). Restricted Liu estimator in generalized linear models: Monte Carlo simulation studies on gamma and Poisson distributed responses. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 4, 1250–1276. https://ajindex.com/articles/529721

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (18)

  1. D. A. Belsley, E. Kuh and R. E. Welsch. Regression diagnostics:Identifying influential data and sources of collinearity, John Wiley and Sons, 1980
  2. A. Ben-Israel and T. N. E. Greville. Generalized inverses: Theory and applications, John Wiley and Sons, 1974
  3. S. Chatterjee and A. S. Hadi. Sensitivity analysis in linear regression, John Wiley and Sons, 1988
  4. F. A. Graybill. Theory and application of the linear model, Duxbury Press, 1976
  5. J. W. Hardin and J. M. Hilbe. Generalized linear models and extensions, Stata Press, 2012
  6. D. A. Harville. Matrix algebra from a statistician’s perspective, Springer, 2008
  7. S. Kaçıranlar, S. Sakallıoğlu, F. Akdeniz, G. P. Styan and H. J. Werner. A new biased estimator in linear regression and a detailed analysis of the widely-analysed dataset on Portland cement, Sankhya: The Indian J Stat Ser B. 61, 443-459, 1999
  8. F. Kurtoğlu and M. R. Özkale. Liu estimation in generalized linear models: application on gamma distributed response variable, Statistical Papers 57(4), 911-928, 2016
  9. K. Liu. A new class of biased estimate in linear regression, Comm Statist Theory Methods 22(2), 393-402, 1993
  10. M. J. Mackinnon and M. L. Puterman. Collinearity in generalized linear models, Comm Statist Theory Methods 18(9), 3463-3472, 1989
  11. B. D. Marx. A continuum of principal component generalized linear regressions, Comput Statist Data Analysis 13, 385-393, 1992
  12. B. D. Marx and E. P. Smith. Principal component estimation for generalized linear regression, Biometrika 77(1), 23-31, 1990
  13. G. C. McDonald and D. I. Galarneau. A monte carlo evaluation of ridge-type estimators, J Amer Statist Assoc. 70, 407-416, 1975
  14. R. H. Myers. Classical and modern regression with applications, Duxbury Press, 1990
  15. H. Nyquist. Restricted estimation of generalized linear models, J Roy Statist Soc Ser C. 40(1), 133-141, 1991
  16. M. R. Özkale. The relative efficiency of the restricted estimators in linear regression models, J App Statist. 41(5), 998-1027, 2014
  17. B. Segerstedt. On ordinary ridge regression in generalized linear models, Commun Statist Theory Methods 21(8), 2227-2246, 1992
  18. G. Trenkler and H. Toutenburg. Mean squared error matrix comparisons between biased estimators an overview of recent results, Statistical Papers 31(1), 165-179, 1990.