Change-point estimation using shape-restricted regression splines

Abstract

We consider estimating a regression function fm and a change-point m, where m is a mode or an inflection point. For a given m, the least-squares estimate of fm is found using constrained regression splines, then the set of possible change-points is searched to find the overall least-squares mˆ. Convergence rates are obtained for each type of change-point estimator, and simulations show that these methods compare well to existing methods. Extensions to the partial linear model and to the case of correlated errors are straightforward, and a penalized spline version is also provided. The methods are available in the R package ShapeChange.