Simple and fast generalized - M (GM) estimator and its application to real data set

Abstract

It is now evident that some robust methods such as MM-estimator do not address the concept of bounded influence function, which means that their estimates still be affected by outliers in the X directions or high leverage points (HLPs), even though they have high efficiency and high breakdown point (BDP). The Generalized M(GM) estimator, such as the GM6 estimator is put forward with the main aim of making a bound for the influence of HLPs by some weight function. The limitation of GM6 is that it gives lower weight to both bad leverage points (BLPs) and good leverage points (GLPs) which make its efficiency decreases when more GLPs are present in a data set. Moreover, the GM6 takes longer computational time. In this paper, we develop a new version of GM-estimator which is based on simple and fast algorithm. The attractive feature of this method is that it only downs weights BLPs and vertical outliers (VOs) and increases its efficiency. The merit of our proposed GM estimator is studied by simulation study and well-known aircraft data set.