The Trimmed Mean in Non-parametric Regression Function Estimation

TL;DR

This paper introduces a trimmed Nadaraya-Watson estimator for non-parametric regression, demonstrating its robustness, asymptotic properties, and practical effectiveness through simulations and real data applications.

Contribution

It proposes a novel trimmed estimator with characterized properties, robustness analysis, and validation through simulations and real data benchmarks.

Findings

Estimator is robust to outliers.

It has desirable asymptotic properties.

Performs well in practical data scenarios.

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.