Robust Estimation of Regression Coefficients with Outliers

Abstract

This study concentrates on the construction of weights for the estimation of regression coefficients in multiple linear regression with outliers using a new proposed influence function. Set of weights, modified weights one (MW1) are obtained from newly modified influence function. The proposed estimates are applied in the M-estimator of the regression coefficients with outliers and compared to ordinary least-squares (OLS) and other M-estimates by simulation. Results of the estimates indicate that the new weights out perform the least squares estimates and the other M-estimates. As for X-outliers and XY-outliers, it is found that the proposed estimates using MW out perform the least squares estimates for all sample sizes. It also gives high values of R² and low MSE at different percentages of outliers as well.