Improving generalized ridge estimator for the gamma regression model.

Section: Research Paper
Issue
Vol. 21 No. 1 (2024): Volume 21 Issue 1
Published
Jun 25, 2025
Pages
102-111

Abstract

It has been consistently proven that the ridge estimator is an effective shrinking strategy for reducing the effects of multicollinearity. An effective model to use when the response variable is positively skewed is the Gamma Regression Model (GRM). However, it is well known that the existence of multicollinearity can have a detrimental impact on the variance of the maximum likelihood estimator (MLE) of the gamma regression coefficients. The generalized ridge estimator is suggested in this study as a solution to the ridge estimator's limitation. The shrinkage matrix has been estimated using a number of different techniques. Our Monte Carlo simulation and actual data application findings indicate that the suggested estimator, regardless of the kind of estimating method of shrinkage matrix, is superior to the MLE and ridge estimator in terms of Mean Square Error (MSE). Additionally, compared to other methods, some shrinkage matrix estimation techniques can significantly enhance results.

References

  1. Al-Abood AM, Young DH. Improved deviance goodness of fit statistics for a gamma regression model. Communications in Statistics - Theory and Methods. 1986;15(6):1865-1874. DOI: 1080/03610928608829223.
  2. Al-Fakih AM, Algamal ZY, Lee MH, et al. QSAR classification model for diverse series of antifungal agents based on improved binary differential search algorithm. SAR QSAR Environ Res. 2019 Feb;30(2):131-143. DOI: 1080/1062936X.2019.1568298. PubMed PMID: 30734580.
  3. Al-Hassan YM. Performance of a new ridge regression estimator. Journal of the Association of Arab Universities for Basic and Applied Sciences. 2010;9(1):23-26.
  4. Alharthi AM, Lee MH, Algamal ZY, et al. Quantitative structure-activity relationship model for classifying the diverse series of antifungal agents using ratio weighted penalized logistic regression. SAR QSAR Environ Res. 2020 Jul 6:1-13. DOI: 1080/1062936X.2020.1782467. PubMed PMID: 32628042.
  5. Alkhamisi MA, Shukur G. A Monte Carlo study of recent ridge parameters. Communications in StatisticsSimulation and Computation. 2007;36(3):535-547.
  6. Amin M, Amanullah M, Aslam M, et al. Influence diagnostics in gamma ridge regression model. Journal of Statistical Computation and Simulation. 2018;89(3):536-556. DOI: 1080/00949655.2018.1558226.
  7. Amin M, Amanullah M, Cordeiro GM. Influence diagnostics in the Gamma regression model with adjusted deviance residuals. Communications in Statistics - Simulation and Computation. 2016;46(9):6959-6973. DOI: 1080/03610918.2016.1222420.
  8. Amin M, Qasim M, Amanullah M, et al. Performance of some ridge estimators for the gamma regression model. Statistical Papers. 2017;61(3):997-1026. DOI: 1007/s00362-017-0971-z.
  9. Amin M, Qasim M, Yasin A, et al. Almost unbiased ridge estimator in the gamma regression model. Communications in Statistics - Simulation and Computation. 2020:1-21. DOI: 1080/03610918.2020.1722837.
  10. Asar Y, Gen A. New shrinkage parameters for the Liu-type logistic estimators. Communications in Statistics - Simulation and Computation. 2015;45(3):1094-1103. doi: 1080/03610918.2014.995815.
  11. Asar Y, Karaibrahimolu A, Gen A. Modified ridge regression parameters: A comparative Monte Carlo study. Hacettepe Journal of Mathematics and Statistics. 2014;43(5):827-841.
  12. Batah FSM, Ramanathan TV, Gore SD. The efficiency of modefied jackknife and ridge type regression estimators - A comparison. Surveys in Mathematics and its Applications. 2008;3:111 122.
  13. Bhat S, Raju V. A class of generalized ridge estimators. Communications in Statistics-Simulation and Computation. 2017;46(7):5105-5112.
  14. De Jong P, Heller GZ. Generalized linear models for insurance data. Vol. 10. Cambridge University Press Cambridge; 2008.
  15. Dorugade A, Kashid D. Alternative method for choosing ridge parameter for regression. Applied Mathematical Sciences. 2010;4(9):447-456.
  16. Dorugade A. New ridge parameters for ridge regression. Journal of the Association of Arab Universities for Basic and Applied Sciences. 2014;15(1):94-99.
  17. Dunder E, Gumustekin S, Cengiz MA. Variable selection in gamma regression models via artificial bee colony algorithm. Journal of Applied Statistics. 2016:1-9. DOI: 1080/02664763.2016.1254730.
  18. Firinguetti L. A generalized ridge regression estimator and its finite sample properties: A generalized ridge regression estimator. Communications in Statistics-Theory and Methods. 1999;28(5):1217-1229.
  19. Hocking RR, Speed F, Lynn M. A class of biased estimators in linear regression. Technometrics. 1976;18(4):425-437.
  20. Hoerl AE, Kennard RW. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics. 1970;12(1):55-67.
  21. Kurtolu F, zkale MR. Liu estimation in generalized linear models: application on gamma distributed response variable. Statistical Papers. 2016;57(4):911-928. DOI: 1007/s00362-016-0814-3.
  22. Lukman AF, Ayinde K, Kibria BMG, et al. Modified ridge-type estimator for the gamma regression model. Communications in Statistics - Simulation and Computation. 2020;1-15. DOI: 1080/03610918.2020.1752720.
  23. Malehi AS, Pourmotahari F, Angali KA. Statistical models for the analysis of skewed healthcare cost data: A simulation study. Health Economics Review. 2015;5:1-11. DOI: 1186/s13561-015-0045-7. PubMed PMID: 26029491; PubMed Central PMCID: PMCPMC4442782.
  24. Mandal S, Arabi Belaghi R, Mahmoudi A, et al. Stein-type shrinkage estimators in gamma regression model with application to prostate cancer data. Stat Med. 2019 Sep 30;38(22):4310-4322. DOI: 1002/sim.8297. PubMed PMID: 31317564.
  25. Mnsson K, Shukur G, Golam Kibria B. A simulation study of some ridge regression estimators under different distributional assumptions. Communications in Statistics-Simulation and Computation. 2010;39(8):1639-1670.
  26. Nomura M. On the almost unbiased ridge regression estimator. Communications in Statistics-Simulation and Computation. 1988;17(3):729-743.
  27. Qasim M, Amin M, Amanullah M. On the performance of some new Liu parameters for the gamma regression model. Journal of Statistical Computation and Simulation. 2018;88(16):3065-3080. DOI: 1080/00949655.2018.1498502.
  28. Troskie C, Chalton D, editors. Detection of outliers in the presence of multicollinearity. Multidimensional statistical analysis and theory of random matrices, Proceedings of the Sixth Lukacs Symposium, eds. Gupta, AK and VL Girko; 1996.
  29. Uusipaikka E. Confidence intervals in generalized regression models. NW: Chapman & Hall/CRC Press; 2009.
  30. Wasef Hattab M. A derivation of prediction intervals for gamma regression. Journal of Statistical Computation and Simulation. 2016;86(17):3512-3526. DOI: 1080/00949655.2016.1169421.

Authors

Zakariya Yahya Algamal

Dept. of Statistics and Informatics/ college of computer sciences and mathematics/ University of Mosul, Mosul, iraq

ORCID
Avan Al-Saffar

Department of Informatics & Statistic, College of Administration and Economics, Salahaddin University, Erbil,, Iraq

ORCID

Identifiers

Download this PDF file
PDF

Statistics

How to Cite

Yahya Algamal, Z., آفان, & Al-Saffar, A. (2025). Improving generalized ridge estimator for the gamma regression model. IRAQI JOURNAL OF STATISTICAL SCIENCES, 21(1), 102–111. Retrieved from https://rjps.uomosul.edu.iq/index.php/stats/article/view/20589