A Bernstein polynomial approach of the robust regression

Abstract

This paper proposes a new family of robust non-parametric estimators for regression functions by applying polynomials to construct a robust regression estimator. Theoretical results and tests on simulated and real data sets validate the efficiency and practicality of the approach. Moreover, some of its asymptotic properties are discussed and demonstrated. Experimental studies are conducted to compare this new approach with the Bernstein-Nadaraya-Watson estimator and the Nadaraya-Watson estimators. Some simulations are performed to illustrate that our robust estimator has the lowest average integrated squared error ($ \overline{AISE} $). In the end, real data is utilized to assess the performance of conventional and newly presented robust regression algorithms regarding their ability to handle sensitivity to outliers.

Keywords

• nonparametric regression
• bernstein polynomial
• robust estimation
• asymptotic normality
• nadaraya-watson estimators