Bias Correction for a Generalized Log-Gamma Regression Model

Abstract

A regression model is considered in which the response variable has the generalized log-gamma distribution. Bias approximations for the maximum likelihood estimators of the regression coefficients and scale parameter are presented. The estimator of the scale parameter has a negative bias, which becomes increasingly marked as the number of regressor variates increases. A bias-corrected estimator is proposed that has improved mean squared error properties provided there is at least one regressor variate. Approximations to the percentiles of the unconditional distributions of pivotal random variables used for statistical inference for the parameters in the log-gamma regression model are proposed and evaluated for the normal error and Type I extreme-value error models. The results suggest that bias correction for the estimate of the scale parameter will be important in small samples for all densities in the log-gamma family.

KEY WORDS:

• Maximum likelihood estimation
• Improved inference procedures
• Confidence intervals