Breakdown plot of symmetry distance based robust estimators

The Least Median Square and Least Trimmed Square are the most popular methods that have a high breakdown point (50%), but when the outliers are clustered, these methods can breakdown at lower percentages of outliers. In this paper, the breakdown property of LMS, LTS and LTSD are investigated with the presence of large percentage of clustered outliers in the data. The concept of symmetry distance (SD) based method is proposed, called the M estimator based symmetry distance (MSD). The superiority of the proposed method has been demonstrated by considering break down property over the LMS, LTS and LTSD methods, when large percentage of clustered outliers and/or a large deviation in the inliers population under real and simulating environment.