An Improved Family of Estimators for Estimating Population Mean Using Robust Regression in the Presence of Outliers

Outliers can be misleading and cause false interpretations of statistical results. Dealing with outliers properly can help with acquiring effective information before drawing a conclusion based on that data. Normality assumption in the traditional least square regression method is one of the standard statistical assumptions that is affected by outliers. Robust regression is a method for estimating regression coefficients in the linear regression model with contaminated data that has outliers in it in order to improve the efficiency of the estimators. In this paper, a family of estimators for finite population mean using robust regression with known parameters of an auxiliary variable that is related to the study variable has been proposed. Expression of the bias and mean square error of the improved family of estimators has been demonstrated using a Taylor series approximation. The simulation studies measure the efficiency of the proposed family of estimators for estimating population mean using the mean square error as a criterion. The simulation results show that the improved family of estimators work well under suitable conditions.