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Performance of some ridge estimators for the gamma regression model

Author

Listed:
  • Muhammad Amin

    (Bahauddin Zakariya University)

  • Muhammad Qasim

    (Bahauddin Zakariya University)

  • Muhammad Amanullah

    (Bahauddin Zakariya University)

  • Saima Afzal

    (Bahauddin Zakariya University)

Abstract

In this study, we proposed some ridge estimators by considering the work of Månsson (Econ Model 29(2):178–184, 2012), Dorugade (J Assoc Arab Univ Basic Appl Sci 15:94–99, 2014) and some others for the gamma regression model (GRM). The GRM is a special form of the generalized linear model (GLM), where the response variable is positively skewed and well fitted to the gamma distribution. The commonly used method for estimation of the GRM coefficients is the maximum likelihood (ML) estimation method. The ML estimation method perform better, if the explanatory variables are uncorrelated. There are the situations, where the explanatory variables are correlated, then the ML estimation method is incapable to estimate the GRM coefficients. In this situation, some biased estimation methods are proposed and the most popular one is the ridge estimation method. The ridge estimators for the GRM are proposed and compared on the basis of mean squared error (MSE). Moreover, the outperforms of proposed ridge estimators are also calculated. The comparison has done using a Monte Carlo simulation study and two real data sets. Results show that Kibria’s and Månsson and Shukur’s methods are preferred over the ML method.

Suggested Citation

  • Muhammad Amin & Muhammad Qasim & Muhammad Amanullah & Saima Afzal, 2020. "Performance of some ridge estimators for the gamma regression model," Statistical Papers, Springer, vol. 61(3), pages 997-1026, June.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-017-0971-z
    DOI: 10.1007/s00362-017-0971-z
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    References listed on IDEAS

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    1. B. Kibria & Kristofer Månsson & Ghazi Shukur, 2012. "Performance of Some Logistic Ridge Regression Estimators," Computational Economics, Springer;Society for Computational Economics, vol. 40(4), pages 401-414, December.
    2. Kibria, B. M. Golam & Månsson, Kristofer & Shukur, Ghazi, 2011. "A Ridge Regression estimator for the zero-inflated Poisson model," Working Paper Series in Economics and Institutions of Innovation 257, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
    3. Månsson, Kristofer & Shukur, Ghazi, 2011. "A Poisson ridge regression estimator," Economic Modelling, Elsevier, vol. 28(4), pages 1475-1481, July.
    4. James W. Hardin & Joseph W. Hilbe, 2012. "Generalized Linear Models and Extensions, 3rd Edition," Stata Press books, StataCorp LP, edition 3, number glmext, March.
    5. Månsson, Kristofer, 2012. "On ridge estimators for the negative binomial regression model," Economic Modelling, Elsevier, vol. 29(2), pages 178-184.
    6. S. le Cessie & J. C. van Houwelingen, 1992. "Ridge Estimators in Logistic Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 191-201, March.
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    Cited by:

    1. Adewale F. Lukman & B. M. Golam Kibria & Cosmas K. Nziku & Muhammad Amin & Emmanuel T. Adewuyi & Rasha Farghali, 2023. "K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    2. Muhammad Qasim, 2024. "A weighted average limited information maximum likelihood estimator," Statistical Papers, Springer, vol. 65(5), pages 2641-2666, July.

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