Non-Parametric Estimation of a Smooth Regression Function

Abstract

Summary This paper presents a new family of non-parametric estimators of a smooth regression function, which are shown to have theoretical advantages in small samples over some alternative estimators. The new estimator has practical computational advantages over spline functions, while its smoothing properties are very close to the optimal smoothing properties of cubic splines. A simulation experiment demonstrates the remarkable success of the cross-validation technique as a means of determining the appropriate degree of smoothing.