Adaptive Estimation Strategies in Gamma Regression Model

  • O. ReangsephetEmail author
  • S. Lisawadi
  • S. E. Ahmed
Original Article


In this study, we considered parameter estimation and inference in the gamma regression model when there exist many covariates, some of which may be treated as a nuisance. We proposed novel estimators based on the pretest and shrinkage strategies and used these to improve the efficiency of estimation. Their asymptotic properties were established. The performance of the proposed estimators was compared with that of the classical estimator through Monte Carlo simulations and application to a real dataset. The pretest and shrinkage estimation strategies were shown to perform well in terms of both parameter estimation and predictive power.


Gamma regression Pretest and shrinkage Asymptotic properties Monte Carlo 



The research work of Professor S. Ejaz Ahmed was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. The authors gratefully acknowledge the financial support provided by Faculty of Science and Technology, Thammasat University.


  1. 1.
    Ahmed SE (1992) Shrinkage preliminary test estimation in multivariate normal distributions. J Stat Comput Simul 43(3–4):177–195MathSciNetCrossRefGoogle Scholar
  2. 2.
    Ahmed SE (2014) Penalty, shrinkage and pretest strategies: variable selection and estimation. Springer, BerlinCrossRefGoogle Scholar
  3. 3.
    Amin M, Qasim M, Amanullah M, Afzal S (2017) Performance of some ridge estimators for the gamma regression model. Statistical papers 1–30Google Scholar
  4. 4.
    Bancroft TA (1944) On biases in estimation due to the use of preliminary tests of significance. Ann Math Stat 15(2):190–204MathSciNetCrossRefGoogle Scholar
  5. 5.
    Baranchik AJ (1970) A family of minimax estimators of the mean of a multivariate normal distribution. Ann Math Stat 41:642–645MathSciNetCrossRefGoogle Scholar
  6. 6.
    Cepeda CE, Corrales M, Cifuentes MV, Zarate H (2016) On gamma regression residuals. JIRSS 15:29MathSciNetzbMATHGoogle Scholar
  7. 7.
    Checkley W, Guzman-Cottrill J, Epstein L, Innocentini N, Patz J, Shulman S (2009) Short-term weather variability in Chicago and hospitalizations for Kawasaki disease. Epidemiology 20(2):194–201CrossRefGoogle Scholar
  8. 8.
    Chitsaz S, Ahmed SE (2012) An improved estimation in regression parameter matrix in multivariate regression model. Commun. Stat. Theory Methods 41(13–14):2305–2320MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hossain S, Ahmed SE, Doksum KA (2015) Shrinkage, pretest, and penalty estimators in generalized linear models. Stat Methodol 24:52–68MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hossain S, Thomson T, Ahmed SE (2018) Shrinkage estimation in linear mixed models for longitudinal data. Metrika 81(5):569–586MathSciNetCrossRefGoogle Scholar
  11. 11.
    Hothorn T (2016) TH's Data Archive. R package version 1.0-7.
  12. 12.
    James W, Stein C (1961) Estimation with quadratic loss. Proc Fourth Berkeley Symp Math Stat Probab 1:361–379MathSciNetzbMATHGoogle Scholar
  13. 13.
    Judge GG, Bock ME (1978) The statistical implications of pre-test and stein-rule estimators in econometrics. North-Holland, AmsterdamzbMATHGoogle Scholar
  14. 14.
    Li Y, Hong HG, Ahmed SE, Li Y (2018) Weak signals in high-dimensional regression: detection, estimation and prediction. Appl Stoch Models Bus Ind 35:283MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lisawadi S, Shah MKA, Ahmed SE (2016) Model selection and post estimation based on a pretest for logistic regression models. J Stat Comput Simul 86(17):3495–3511MathSciNetCrossRefGoogle Scholar
  16. 16.
    Mittlböck M, Heinzl H (2002) Measures of explained variation in gamma regression models. Commun Stat Simul Comput 31(1):61–73MathSciNetCrossRefGoogle Scholar
  17. 17.
    Myers RH, Montgomery DC, Vining GG, Robinson TJ (2012) Generalized linear models: with applications in engineering and the sciences, vol 791. Wiley, LondonzbMATHGoogle Scholar
  18. 18.
    Reangsephet O, Lisawadi S, Ahmed SE (2018) Improving estimation of regression parameters in negative binomial regression model. In: International conference on management science and engineering management. Springer, pp 265–275Google Scholar
  19. 19.
    Stein C (1956) The admissibility of Hotelling’s \(t^{2}\)-test. Ann Math Stat 27(3):616–623CrossRefGoogle Scholar
  20. 20.
    Verburg IWM, de Keizer NF, de Jonge E, Peek N (2014) Comparison of regression methods for modeling intensive care length of stay. PLoS ONE 9(10):e109684CrossRefGoogle Scholar
  21. 21.
    Winkelmann R (2008) Econometric analysis of count data. Springer, BerlinzbMATHGoogle Scholar
  22. 22.
    Yüzbaşı B, Ahmed SE, Aydın D (2017) Ridge-type pretest and shrinkage estimations in partially linear models. Statistical papers 1–30Google Scholar
  23. 23.
    Yüzbaşı B, Arashi M (2017) Double shrunken selection operator. Commun Stat Simul Comput 48(3):666–674MathSciNetCrossRefGoogle Scholar
  24. 24.
    Yuzbasi B, Arashi M, Ahmed S E (2017) Big data analysis using shrinkage strategies. arXiv preprint arXiv:1704.05074

Copyright information

© Grace Scientific Publishing 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThammasat UniversityPathum ThaniThailand
  2. 2.Department of Mathematics and StatisticsBrock UniversitySt. CatharinesCanada

Personalised recommendations