M-Estimation Use Bisquare, Hampel, Huber, and Welsch Weight Functions in Robust Regression

Abstract

The estimation by the least squares method (LSM) is often used in simple or multiple regression model. However, it was not uncommon for the response variables  in model  which contain contamination or outliers. LSM is known will be very sensitive to these problem, so if LSM is still used in regression then parameter estimate can be bias. Robust regression is well known as a method that robust from effect of outliers in order to obtain better result from LSM. The paper will discuss the methods of M-estimation to model the response data which contain the outliers using Bisquare, Hampel, Huber, and Welsch weight function using simulation data and HDI (Human Development Index) data in West Java Province. On the HDI data, the M estimations prediction method with the Welsch weight function yields , the best of other weight functions.