Regression spline smoothing using the minimum description length principle

Abstract

One approach to estimating a function nonparametrically is to fit an rth-order regression spline to the noisy observations, and one important component of this approach is the choice of the number and the locations of the knots. This article proposes a new regression spline smoothing procedure which automatically chooses: (i) the order r of the regression spline being fitted; (ii) the number of the knots; and (iii) the locations of the knots. This procedure is based on the minimum description length principle, which is rarely applied to choose the amount of smoothing in nonparametric regression problems.