A Simple Roughness Penalty Approach to Regression Spline Estimation

A regression spline is a piecewise polynomial function whose highest order nonzero derivative takes jumps at xed \knots." Usually regression splines are smoothed by deleting nonessential knots, or equivalently setting the jumps at those knots to zero. A method that is simpler to implement and has lower computational cost is to shrink the jumps at all knots towards zero by using a penalty function. The method is widely applicable, e.g., to multivariate regression , interaction models, and semiparametric estimators. We also consider a Bayesian approach with a new type of nonparametric prior.