Robust Nonparametric Regression Using Kernel Smoothing

Abstract

We consider the application of nonparametric kernel smoother with the presence of outliers. Previous researches in similar fields have been focused on the direct application of Huber's M-estimator in the nonparametric methods, which is both computationally and theoretically difficult. Besides, the traditional M-estimator defines a fixed cut-off value, which may not be efficient for data with non-constant variation. To address these problems, we adopt the idea of pseudo data, with the implementation of which, the robust estimate can be obtained from least squares kernel smoother. We also propose to select the cut-off value of the M-estimator according to the local variation of the data. Results from theoretical exercise show that the pseudo data and a least squares kernel smoother is equivalent to the classical robust kernel smoother. Simulation studies suggest that the robust kernel smoother with non-constant cut-off value leads to a superior mean squared error performance compared to fixed cut-off value.