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Robustness of two-phase regression tests. (English) Zbl 1135.62352
Summary: This article studies the robustness of different likelihood ratio tests proposed by R. E. Quandt [J. Am. Stat. Assoc. 53, 873–880 (1958; Zbl 0116.37304); J. Am. Stat. Assoc. 55, 324–330 (1960; Zbl 0095.13602)], (Q-Test), H.-J. Kim and D. Siegmund [Biometrika 76, No.3, 409-423 (1989; Zbl 0676.62027)], (KS-Test), and H.-J. Kim [Commun. Stat., Theory Methods 22, No. 3, 647–657 (1993; Zbl 0800.62377)], (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.

62J05 Linear regression; mixed models
62F03 Parametric hypothesis testing
62F35 Robustness and adaptive procedures (parametric inference)
62J02 General nonlinear regression