In this article, we consider testing a general linear hypothesis for a regression model when the error distribution belongs to the class of spherical distributions. The distributional robustness of the F-statistics under a null hypothesis for spherically symmetric distributions is well understood. This invariance property, however, does not hold under the alternative hypothesis. Motivated by a simplified example, we study the relationship between power of the test and the error distribution's dispersion and kurtosis. We find that these two parameters are not sufficiently precise measures for determining the power behavior of a test.
- Elliptically and spherically symmetric distributions
- Linear models
- Tail behavior