Minimum Covariance Determinant-Based Quantile Robust Regression-Type Estimators for Mean Parameter

Robust regression tools are commonly used to develop regression-type ratio estimators with traditional measures of location whenever data are contaminated with outliers. Recently, the researchers extended this idea and developed regression-type ratio estimators through robust minimum covariance determinant (MCD) estimation. In this study, the quantile regression with MCD-based measures of location is utilized and a class of quantile regression-type mean estimators is proposed. The mean squared errors (MSEs) of the proposed estimators are also obtained. The proposed estimators are compared with the reviewed class of estimators through a simulation study. We also incorporated two real-life applications. To assess the presence of outliers in these real-life applications, the Dixon chi-squared test is used. It is found that the quantile regression estimators are performing better as compared to some existing estimators.