An M Estimation Based on Outliers Separation

The key issue of robust M estimation is to construct equivalent weights based on residuals to down-weight outlying observations. However, the correlation of residuals may cause incorrectly down-weighting normal observations. Therefore, this paper aims to propose an M estimation that down-weights outlying observations based on outliers separation. The results of two examples show that the proposed method has high stability. Meanwhile, it can correctly locate the position of outliers even if the outlier rate is as high as 1/3.