Weighted Trimean as a Regressor in the Estimate of Theil-Sen Regression

Abstract

The most used method in nonparametric regression analysis is the Theil-Sen approach. With this method, all coefficient estimations are made with the median parameter as opposed to parametric methods. The most important criticism in computations with the median parameter is that the impact of extreme values does not participate in calculations.  In this study, it was proposed to use the trimean parameter by weighting, which more effectively adds the effect of outliers to the average account in Theil-Sen regression analysis. In applications with 5 data sets, Theil-Sen calculations with weighted trimean were found to be more successful than calculations with the median parameter. Thus, in cases where the outliers are too high or directly affect the data, it can be said that the use of weighted trimean will yield more effective results