Adjusted Optimal Trimmed Theil-Sen Method for Multiple Regression Model, with Outliers Detection and Management

Abstract

The objective of this research was to propose the adjusted optimal trimmed Theil-Sen (AOTS) method and compare the efficiency, with outliers, of four parametric and two nonparametric statistical point estimation methods for multiple regression analysis. The parametric methods consisted of the following: Ordinary Least Squares (OLS), Ordinary Least Trimmed Squares (OLTS), Parametric Bootstrap (PB), and Jackknife (JK) methods. The nonparametric methods consisted of Optimal Theil-Sen (OTS) and proposed AOTS methods. Data were simulated in a randomized manner in three instances of simulation: one, simulation of independent variables and errors without outliers; two, simulation of independent variables with outliers; and three, simulation of errors with outliers. Outliers were detected by an Interquartile Range (IQR) method. Both ends of the data were truncated to deal with outliers. Y-intercept and regression coefficient were estimated with six estimation methods. The measure for comparing the performances of these methods was a mean square error. For the parametric methods, when the independent variables had outliers with normal distribution, the PB method provided the least mean square error. It would be a good substitute for the OLS method. When the errors had outliers, for all normal, uniform, and gamma distributions, the performance of the OLTS method was better than the OLS method. For the nonparametric methods, when the independent variables had outliers with normal or uniform distributions, the proposed AOTS method performed better than the OTS method. In the same way, when the independent variables had outliers with gamma distribution, the proposed AOTS methods performed competitively to the OTS method. However, when the errors had outliers with normal, uniform, or gamma distribution, the OTS method edged over the proposed AOTS method.