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Estimation of a common slope in a gamma regression model with multiple strata: An empirical Bayes method

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  • Minoda, Yuta
  • Yanagimoto, Takemi

Abstract

An empirical Bayes method for a gamma regression model with a slope parameter [beta] common through multiple strata is proposed and examined. Assuming that the number of strata is fairly large, we attempt to modify a usual empirical Bayes method so as to yield an improved estimator of [beta]. Such a modification is necessary to pursue compromise between Bayesian and frequentist approaches. Simulation studies strongly support superiority of the proposed estimator over the maximum likelihood estimator. A test for [beta]=0 is also discussed. To show large difference between the two estimates, an illustrative example is given.

Suggested Citation

  • Minoda, Yuta & Yanagimoto, Takemi, 2009. "Estimation of a common slope in a gamma regression model with multiple strata: An empirical Bayes method," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4178-4185, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4178-4185
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    References listed on IDEAS

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    1. Bradley Efron, 2005. "Bayesians, Frequentists, and Scientists," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1-5, March.
    2. Takemi Yanagimoto & Eiji Yamamoto, 1991. "Constructing elementary procedures for inference of the gamma distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(3), pages 539-550, September.
    3. Alan Agresti & Yongyi Min, 2005. "Frequentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2 × 2 Contingency Tables," Biometrics, The International Biometric Society, vol. 61(2), pages 515-523, June.
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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    Cited by:

    1. Wang, Lichun & Singh, Radhey S., 2014. "Linear Bayes estimator for the two-parameter exponential family under type II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 633-642.

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