THEIL-SEN REGRESSION ESTIMATORS WITH TRIMEAN FAMILY

Theil-Sen regression can be defined as a robust method that is frequently used in non-parametric regression analysis. In this method, In this method, parameter estimations are made with the median parameter. Trimean is a measure of central tendency that can be used in data especially when there are agglomeration or outliers and it is a variation of mean based on quartiles. In this article it is proposed similar means with the help of other quantile values and they are defined as trimean family means: Tetramean, pentamean, hexamean, heptamean, octamean, nonamean and decamean. With these newly defined means, parameter estimations were made in Theil-Sen regression and the results were compared with the classical Theil-Sen estimation results. In the application, datasets derived from 7 different distributions and 3 different datasets studied in the literature were used. According to the results obtained, trimean family results in real life data and median parameter results in simulation data were more successful. According to the results of the analysis, if there are no significant outliers in the data, it can be said that the results of the trimean family parameters are effective.