299 – Nonlinear Models and Other Optimization Problems
Robust Regression by Self-Updating Process
Ting-Li Chen
Academia Sinica
Robust regression aims to reduce the effect from outliers. One standard approach is to perform weighted regression in which the weights are iteratively updated according to the new fitted line. In this paper, we will present an iterative process to reduce the effect from outliers. It is an extension of SUP clustering algorithm (Chen and Shiu, 2007). This process updates both the weights and the data points through iterations. At each iteration, a line is fitted locally for each data point. The data point is then moved to this line. Throughout this process, all data points except outliers will gradually move to form a line. We will show results from simulation studies that our proposed method outperforms the standard approach. The success of the proposed algorithm comes from its two important properties: One is that the local estimation can reduce the effect from outliers so that the method is more robust. The other is that moving data based on the current estimation can improve the overall efficiency.