SKEWNESS FOR PARAMETERS IN GENERALIZED LINEAR MODELS

Abstract

In this paper we give an asymptotic formula of order n ^−1/2, where n is the sample size, for the skewness of the distribution of the maximum likelihood estimates of the linear parameters in generalized linear models. The formula is given in matrix notation and is very suitable for computer implementation. Several special cases are discussed. We also give asymptotic formulae for the skewness of the distribution of the maximum likelihood estimates of the dispersion and precision parameters.

Keywords:

• Asymptotic expansion
• Canonical link
• Dispersion parameter
• Generalized linear model
• Maximum likelihood estimate
• Precision parameter
• Skewness

ACKNOWLEDGMENTS

We thank an anonymous referee and an associated editor for useful suggestions. We gratefully acknowledge financial support from the Brazilian agency CNPq.