Robust M-estimation using the equivalent weights constructed by removing the influence of an outlier on the residuals

The key issue in robust M-estimation is to construct the equivalent weights using the residuals of observations for down-weighting the outlying observations. However, the residuals of good observations are also possibly impacted by neighbouring outliers, thus directly down-weighting an observation according to its residual is not theoretically rigorous. Therefore, this paper focuses on the construction of equivalent weights for down-weighting the outlying and doubtful observations by removing the influence of the outlier on the correlated residuals. A down-weighting strategy using the corrected residuals to form the down-weighting factors is proposed. A simulated experiment and a practical experiment are respectively conducted to demonstrate the performances of the proposed down-weighting strategy compared to the direct down-weighting strategy (DDS) and recursive down-weighting strategy (RDS). The results show that the estimated performance of the proposed down-weighting strategy is comparable to that of ...