Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression function, the shape-restricted regression splines are much more robust to knot choices. Monotone regression splines were introduced by Ramsay (1988). In this paper a more numerically efficient computational method is developed, and the method is extended to convex constraints. The restricted versions have smaller squared error loss, if the underlying regression function indeed follows the imposed constraints. The relatively small degrees of freedom and the insensitivity of the fits to the knot choices allow for practical inference methods. Tests of constant versus increasing and linear versus convex regression function, wen implemented with shape-restricted regression splines, have higher power than the standard version using ordinary shape-restricted regression. A test for linear versus increasing regression function is presented. Real-world examples demonstrate the utility of shape-restricted regression splines.
Inference Using Shape-Restricted Regression Splines