A new GM-estimate with high breakdown point

Abstract

The breakdown point of GM-estimators does not exceed 1/(p+1) where p is dimension of explanatory variables in linear regression. One proposes a new version of the GM-estimation with a high breakdown point (HBGM) to provide high resistance against leverage points and vertical outliers. This paper presents a technique aimed at routinely normalized and robustified Euclidean distance among data points for finding leverage points and gross errors in the x- and y-directions, respectively. In addition, a graphical visualization is simultaneously used to display which points are leverage and gross error. Finally, weights of flagged data points will be decreased to a certain value before applying M-estimator. Since robustification and normalization procedures are completely based on the median estimator with the highest breakdown point, the proposed method has a conditional breakdown point of 50% theoretically. The technique was tested with simulated data and also real data set containing the series of landslide deformation. Tests were performed for linear regression models including different scenarios. Consequently, the experimental results showed that the proposed method reaches up to a 50% of breakdown point. Morever, the HBGM method is less time- consuming in parameter estimation.