Least trimmed euclidean deviations for robust leverage in regression estimates

Usually, in the regression models, the data are contaminated with unusually observations (outliers). For that reason the last 30 years have developed robust regression estimators. Among them some of the most famous are Least Trimmed Squares (LTS), MM, Penalized Trimmed Square (PTS) and others. Most of these methods, especially PTS, are based on initial leverage, concerning x outlying observations, of the data sample. However, often, multiple x-outliers pull the distance towards their value, causing leverage bias, and this is the masking problem. In this work we develop a new algorithm for robust leverage estimate based on Least Trimmed Euclidean Deviations (LTED). Extensive computational, Monte-Carlo simulations, with varying types of outliers and degrees of contamination, indicate that the LTED procedure identifies successfully the multiple outliers, and the resulting robust leverage improves significantly the PTS performance.