Annals of Applied Statistics

Inference using shape-restricted regression splines

Mary C. Meyer

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Abstract

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 Ramsay [Statist. Sci. 3 (1998) 425–461], 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 function, when implemented with shape-restricted regression splines, have higher power than the standard version using ordinary shape-restricted regression.

Article information

Source
Ann. Appl. Stat., Volume 2, Number 3 (2008), 1013-1033.

Dates
First available in Project Euclid: 13 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1223908050

Digital Object Identifier
doi:10.1214/08-AOAS167

Mathematical Reviews number (MathSciNet)
MR2516802

Zentralblatt MATH identifier
1149.62033

Keywords
Cone projection convex regression isotonic regression monotone regression nonparametric regression semi-parametric smoothing

Citation

Meyer, Mary C. Inference using shape-restricted regression splines. Ann. Appl. Stat. 2 (2008), no. 3, 1013--1033. doi:10.1214/08-AOAS167. https://projecteuclid.org/euclid.aoas/1223908050


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