Robust mean estimation via auxiliary-informed quantile regression: A modern statistical framework

Abstract

To handle outliers in data, researchers increasingly use robust regression techniques since traditional methods like ordinary least squares are sensitive to outliers/extreme values. Quantile regression is being widely applied in survey  sampling to obtain more reliable and efficient estimates. This study proposes a novel family of quantile regression-ratio-type estimators that incorporate auxiliary information to estimate the finite population mean under simple random sampling. We derived mathematical expressions for bias, mean squared error (MSE), and minimum MSE. Furthermore, we conducted numerical illustrations to confirm these theoretical findings using diverse real-life data sets from various fields such as agriculture loan, cereal nutrition, population, agriculture, and school education. Additionally, a Monte Carlo simulation study based on these real-life data sets is also added to check the performance of the proposed estimators. The numerical findings endorse the effectiveness of the proposed estimators compared to competing estimators. Ultimately this research provides the researcher with a tool to obtain a more precise population mean estimate, which is highly applicable across various scientific disciplines.