Spatially adaptive regression splines and accurate knot selection schemes

Spline procedures have proven effective in estimating smooth functions. How ever, spline procedures based on stepwise addition and/or deletion have som e drawbacks. They suffer from the knot compounding problem, making their pe rformance suboptimal. Furthermore, due to computational complexity, spline procedures may not achieve their full potential. In this article, we propos e a novel knot selection algorithm for regression spline estimation in nonp arametric regression. The algorithm includes three new components: knot rel ocation, guided search, and local fitting. The local properties of the spli ne functions are used to efficiently implement the algorithm. Extensive sim ulation studies are performed to demonstrate the improvement of the new kno t selection algorithm over the stepwise addition and deletion scheme, and t he advantages of the spline procedure with the new knot selection scheme ov er alternative adaptive methods. In the simulations, our procedure achieves very competitive performance with alternative methods and has substantial advantage in nonsmooth functions. Finally, the usefulness of the proposed m ethod is illustrated by an application to signal recovery in speech signal processing.