Robust Techniques to Estimate Parameters of Linear Models

Abstract

Standard regression technique uses Ordinary Least Square estimator (OLS) for model fitting. In the presence of outliers OLS fits the model vary sharply with respect to actual regression curve. For model fitting, this paper applies robust estimation approach as a substitute for OLS. This approach reduces the ill effect of outliers and learns the representation of data. Various robust regression techniques, namely, L estimators, M estimators, S estimator and MM estimator have been used which works on the principle of order statistics and weighting techniques to reduce the weight of distant observations. These estimators are applied on four data set out of which 3 are taken from UCI repository and one is taken from NASA Surface meteorology and Solar energy. When comparing the methods on the basis of bias and variance parameters MM estimator performs well in majority of the data set while in some cases M estimator also exhibited promising results.