Exponentially quantile regression-ratio-type estimators for robust mean estimation

Abstract

Traditional ordinary least square (OLS) regression is commonly utilized to develop regression-ratio type estimators with traditional and non traditional measures of location. However, when data are contaminated by outliers, the ordinary least square estimates become inappropriate, and the alternative approach is to use the robust regression method. To solve this issue, the use of robust regression tools for mean estimation is a commonly settled practice. In the present study, we have proposed an efficient family of exponential quantile regression-ratio type estimators by using the auxiliary information for estimating the finite population mean under simple random sampling scheme. Here it is worth noting that quantile regression is robust to outliers. Mathematical expressions such as bias, mean squared error (MSE), and minimum mean squared error are derived up to first order of approximation. To support theoretical findings, two real data collections originating from different sources are used for numerical illustration. The results are showing the superiority of proposed exponential quantile robust regression family of estimators as compared to the existing estimators under simple random sampling scheme.