Theil-Sen Estimators in a Multiple Linear Regression Model

In this article, we propose the Theil-Sen estimators of parameters in a multiple linear regression model based on a multivariate median, generalizing the Theil-Sen estimator in a simple linear regression model. The proposed estimator is shown to be robust, consistent and asymptotically normal under mild conditions, and super-efficient when the error distribution is discontinuous. It can be chosen to satisfy the prespecified possible robustness and efficiency. Simulations are conducted to compare robustness and efficiency with least squares estimators and to validate super-efficiency. Additionally we obtain a sufficient and necessary condition which characterizes the symmetry of a random vector.