Improved Score Tests in Symmetric Linear Regression Models

Abstract

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n ^−3/2), n being the sample size. The corrections represent an improvement over the corresponding original Rao's score statistics, which are chi-squared distributed up to errors of order O(n ⁻¹). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Keywords:

• Asymptotic distribution
• Bartlett-type correction
• Chi-squared distribution
• Score test
• Symmetric distribution
• t distribution

Mathematics Subject Classification:

• Primary 62F05
• Secondary 62J05

Acknowledgments

We gratefully acknowledge the partial financial support from the following Brazilian agencies: CNPq and FAPESP.