Robust Algorithms for Change-Point Regressions Using the <i>t</i>-Distribution

Abstract

Regression models with change-points have been widely applied in various fields. Most methodologies for change-point regressions assume Gaussian errors. For many real data having longer-than-normal tails or atypical observations, the use of normal errors may unduly affect the fit of change-point regression models. This paper proposes two robust algorithms called EMT and FCT for change-point regressions by incorporating the t-distribution with the expectation and maximization algorithm and the fuzzy classification procedure, respectively. For better resistance to high leverage outliers, we introduce a modified version of the proposed method, which fits the t change-point regression model to the data after moderately pruning high leverage points. The selection of the degrees of freedom is discussed. The robustness properties of the proposed methods are also analyzed and validated. Simulation studies show the effectiveness and resistance of the proposed methods against outliers and heavy-tailed distributions. Extensive experiments demonstrate the preference of the t-based approach over normal-based methods for better robustness and computational efficiency. EMT and FCT generally work well, and FCT always performs better for less biased estimates, especially in cases of data contamination. Real examples show the need and the practicability of the proposed method.

Keywords

• change-point regression
• robust
• <i>t</i>-distribution
• outlier
• EMT algorithm
• FCT algorithm