Inference using shape-restricted regression splines. (English) Zbl 1149.62033

Summary: 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 robust to knot choices. Monotone regression splines were introduced by J. O. Ramsay [Stat. Sci. 3, 425–461 (1998)], but were limited to quadratic and lower order.
In this paper, an algorithm for the cubic monotone case is proposed, and the method is extended to convex constraints and variants such as increasing-concave. The restricted versions have smaller squared error loss than the unrestricted splines, although they have the same convergence rates. The relatively small degrees of freedom of the model and the insensitivity of the fits to the knot choices allow for practical inference methods; the computational efficiency allows for back-fitting of additive models. Tests of constant versus increasing and linear versus convex regression functions, when implemented with shape-restricted regression splines, have higher power than the standard version using ordinary shape-restricted regression.


62G08 Nonparametric regression and quantile regression
65C60 Computational problems in statistics (MSC2010)


pchip; SemiPar
Full Text: DOI arXiv


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