Robustness of two-phase regression tests

Abstract

This article studies the robustness of different likelihood ratio tests proposed by Quandt ([1]) and ([2]), (Q-Test), Kim and Siegmund ([3]), (KS-Test), and Kim ([4]), (K-Test), to detect a change in simple linear regression models. These tests are evaluated and compared with respect to their performance taking into account different scenarios, such as, different error distributions, different sample sizes, different locations of the change point and departure from the homoscedasticity. Two different alternatives are considered: i) with a change in the intercept from one model to the other with the same slope and ii) with a change in both the intercept and slope. The simulation results reveal that the KS-Test is superior to the Q-Test for both models considered while the K-Test is more powerful than the other two tests for nonhomogeneous models with a known variance.