Asymptotic Normality of the Robust Equivariant Estimator for Functional Nonparametric Models

Abstract

As in parametric regression, nonparametric kernel regression is essential for examining the relationship between response variables and covariates. In both methods, outliers may affect the estimators, and hence robustness is essential to deal with practical issues. This paper proposes a family of robust nonparametric estimators with unknown scale parameters for regression function based on the kernel method. In addition, we establish the asymptotic normality of the estimator under the concentration properties on small balls of probability measure of the functional explanatory variables. The superiority of the proposed methods is shown through numerical and real data studies to compare the sensitivity to outliers between the classical and robust regression (fixed and unknown scale parameter). Such a new proposed method will be useful in the future for analyzing data and making decisions.