Estimation of regression coefficients with outliers

Abstract

In linear models, the ordinary least squares estimators of have always turned out to be the best linear unbiased estimates. When the sample data contain outliers, the outliers may have a considerable effect on the least-squares estimates of , and an alternative approach to the problem is needed to obtain a better fit of the model or more precise estimates of . In this study, new weights were constructed for the sample data from two new influence functions and applied in the estimation of regression coefficients with outliers. Two sets of weights, modified weight one (MW1) and modified weight two (MW2), were obtained and applied to the Mestimates of the regression coefficients with outliers so that the effects of the outliers would be lessinfluential. The estimates were compared with the least-squares and other M-estimates by simulation. It was found that the estimates using MW1 have a tendency to give larger values of coefficients of determination than the others, for all sample sizes and with any percentage of X-outliers, Y-outliers or XY-outliers. The MW2 was superior to MW1 in cases of large sample sizes and high percentages of X-outliers. It also performed well for small sample sizes and with low percentages of Y-outliers and XY-outliers. The mean squares errors obtained from MW1 and MW2 were smaller than the others for all sample sizes and with any percentage of X-outliers, Y-outliers and XY- outliers. MW1 worked better than MW2 for all sample sizes and with any percentage of X-outliers, but MW2 was better than MW1 for small or medium sample sizes and with any percentage of Y-outliers or XY-outliers.