Are Regression Series Estimators Efficient in Practice? A Computational Comparison Study

Abstract

This paper is concerned with the practical performances of series-type estimators of a regression function. For different choices of orthonormal bases (Legendre polynomials, trigonometric functions, wavelets) we compare, by simulation arguments, the performances of series-type estimators with the results obtained by two of the most popular nonparametric regression estimation methods: kernel estimation and least-squares cubic splines. It will be shown that orthonormal series estimators are competitive in relation to these former nonparametric procedures. No agreement has emerged on the best method, the results being highly dependent on the nature of the estimated regression function.

Keywords: Nonparametric regression, orthonormal series estimators, kernel smoothing, least-squares cubic splines, wavelets