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Volume :14 Issue : 2 1987      Add To Cart                                                                    Download

Bias-corrected maximum likelihood inference for individual regression coefficients in a gamma regression model

Auther : SAAD T. BAKIR AND DAVID H. YOUNG

Department of Mathematics, University of Kuwait, P.O. Box: 5969, Safat, 13060, Kuwait: and Department of Mathematics and Statisitcs, Brunel University, Uxbridge, U.K.
 

ABSTRACT

 

Bias approximations for the maximum likelihood estimator of the regression coefficients and precision parameter in a gamma regression model are developed. A bias-corrected estimator for the precision parameter is proposed and shown to have markedly better variance and mean square error properties than the maximum likelihood estimator. The standard large sample maximum likelihood inference procedures for a specified individual regression coefficient are examined by theoretical approximation and by simulation and shown to give actual confidence coefficients appreciably smaller than nominal values in small samples when a logarithmic link is assumed. Modified procedures are considered in which the maximum likelihood estimate of the precision parameter is replaced by (i) an estimator based on the deviance which is used in the statistical computing package GLIM, (ii) an estimator based on the Pearson statistic, (iii) the bias-corrected estimator. The use of the first and third estimators is shown to give much better control in small samples over actual confidence coefficients in confidence interval estimation and actual significance levels in testing. procedures are considered in which the maximum likelihood estimate of the precision parameter is replaced by (i) an estimator based on the deviance which is used in the statistical computing package GLIM, (ii) an estimator based on the Pearson statistic, (iii) the bias-corrected estimator. The use of the first and third estimators is shown to give much better control in small samples over actual confidence coefficients in confidence interval estimation and actual significance levels in testing.

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