Current Methods and Applications in Econometrics
Use of Weighted Median in THEIL-SEN Regression AnalysisNecati Alp Erilli
Regression analysis; is one of the most used analytical techniques in statistical prediction studies. The aim of regression analysis; to investigate the relationship between the dependent and independent variable or variables, which is estimated to have a cause-effect relationship between them, to explain the assumed relationship between variables functionally and to define this relationship with a model. Non-parametric regression analysis is a method used in cases where some assumptions that are valid for parametric regression methods cannot be met and give successful results. Nonparametric methods make calculations with the median parameter instead of arithmetic mean. The median parameter does not reflect the effect of outliers on the calculations. Weighted Median calculates the contribution of outlier values to the model even though it gives weight to each observation value. In this study, the Weighted Median parameter was used in the Theil-Sen method which is frequently used in nonparametric regression analysis. Optimum and Hodges-Lehmann calculations which are used in the computation of constant parameters in the Theil-Sen method are also used in this study. The results obtained from Theil-Sen, Hodges-Lehmann and Optimum method used with Weighted Median were tested in different data structures. Thus, the advantages or weaknesses of the use of the weighted median parameter in the Theil-Sen method over the classical methods were determined.