Regression splines are smooth, flexible, and parsimonious nonparametric function estimators, but the fits are sensitive to the choice of the number and placement of the knots. When a priori knowledge about the regression function includes monotonicity or convexity as well as smoothness, the shape-restricted versions of the regression splines may be used. These fits are more satisfactory as they satisfy shape requirements, with the additional benefit of insensitivity to the knot choices. Hypothesis tests of constant versus increasing regression function and linear versus convex may be formulated using the shape-restricted regression splines as the alternative fit. Simulations show that the fits generally have smaller squared error loss compared to the smoothing spline with generalized cross-validation choice of the smoothing parameter. Further simulations show that the hypothesis tests have consistently higher power than the versions using standard shape-restricted regression. Finally, simulations show that the decision to accept or reject is not sensitive to the know choices.
Shape-Restricted Regression Splines