Sign depth for parameter tests in multiple regression

Abstract

This thesis deals with the question how the sign depth test can be applied in the case of multiple regression. Because the result of this test depends on the ordering of the residuals and most times no inherent order is available for multidimensional values one has to think about suitable methods to order these values. In this thesis 13 different ordering methods are described, analyzed and compared with respect to characteristics, computational behavior and performance when using them in the context of sign depth tests. For the last one, several simulations of power functions for many different settings have been carried out. In the simulations different data situations as well as different multiple regression models and different parameters of the sign depth were examined. It is shown in this thesis that a group of so-called “distance based ordering methods” performs best and leads to satisfying results of the sign depth test. Also compared to other tests for regression parameters like the Wald test or the classical sign test the sign depth test performs satisfyingly and especially in the case of testing for model checks it performs clearly better. In addition, this thesis describes the contents and functionality of the R -package GSignTest which was written for this thesis and contains implementations of the sign depth, the sign depth test and the different ordering methods.