The Trimmed Mean in Non-parametric Regression Function Estimation

Abstract

This article studies a trimmed version of the Nadaraya-Watson estimator to estimate the unknown non-parametric regression function. The characterization of the estimator through minimization problem is established, and its pointwise asymptotic distribution is also derived. The robustness property of the proposed estimator is also studied through breakdown point. Besides, the asymptotic efficiency study along with an extensive simulation study shows that this estimator performs well for various cases. The practicability of the estimator is shown for three benchmark real data as well.