Statistical hypothesis testing within the Generalized Error Distribution: Comparing the behavior of some nonparametric techniques

Abstract

This paper’s goal is to deal with the issue of hypothesis testing when the errors are assumed to be distributed according to a Generalized Error Distribution. Focus is given to the central tendency parameters, validating the suitability of nonparametric methods in this respect. The present work describes a simulation study aimed at assessing the validity of the Van der Waerden and Wilcoxon tests in the case of data coming from a G.E.D.; in order to compare the statistical power of such tests, we proceed to calculate the usual empirical significance level. The use of test statistics obtained by means of a Van der Waerden test generalized by considering the G.E.D.’s shape parameter provides better results, in terms of statistical power, compared to the Wilcoxon and the classic Van der Waerden test