Please use this identifier to cite or link to this item:
|Title:||Improved estimators for the shape parameter in gamma regression|
|Citation:||Maths Technical Papers (Brunel University). February 1986, pp 1-27|
|Abstract:||A regression model is considered in which the response variables have gamma distributions with a common shape parameter. A review is given of existing estimators for the shape parameter. Bias expressions for the maximum likelihood estimates of the regression coe f f i c i ent s and the shape parameter are developed. A new estima t o r f o r t h e shape parameter based on bias correction for the maximum likelihood estimator is shown to have markedly better variance and mean square error properties in small to moderate sized samples. Approximations to the low order moments of the Pearson statistic are derived for gamma regression models with general link functions. These are used for the case of a logarithmic link to develop new estimators for the shape parameter which have better moment properties than the estimators based on the Pearson statistic which have been used previously. Finally, the small sample variance and mean square error efficiencies of the estimators relative to the maximum likelihood estimator are evaluated by simulation for the case of a single explanatory variable and a logarithmic link, for a range of sample sizes less than or equal to 100.|
|Appears in Collections:||Dept of Mathematics Research Papers|
Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.