INFERENCE USING SHAPE-RESTRICTED REGRESSION SPLINES
By Mary C. Meyer. 2008
203 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/ac3f07e7fcf4267c118c5898adde7bd54d9f7df7
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In Geometry and Topology
In Statistics and Probability
- Natalya Pya
- Simon N. Wood
- Lauren Hannah
- David B. Dunson
- Warrren B Powell
- Mary C. Meyer
- G. Simpson
- Richard J. Samworth
Citations in the corpus
- Nonparametric Shape-Restricted Regression (2017, unknown): “, [63, 91, 105] (and the references therein) where kernel-based methods have been combined with shape-restrictions, and see [82, 94, 102, 106] where splines are used in conjunction with the shape constraints.”
- Constrained penalized splines (2012, methodology): “Wang & Meyer (2011) propose a formal hypothesis test for monotone versus nonmonotone regression function using constrained and unconstrained splines, and a simulated distribution of a test statistic.”
- Shape constrained additive models (2015, background): “…the first subsection of S.6 shows comparative study with the constrained P-spline regression (Bollaerts et al. 2006), monotone piecewise quadratic splines of Meyer (2008), and shape-restricted penalized B-splines of Meyer (2012) on simulated example on univariate single smooth term models.”
- Multivariate convex regression with adaptive partitioning (2011, methodology): “Key words: Nonparametric regression, shape constraint, convex regression, treed linear model, adaptive partitioning”
- Semiconvex Regression for Metamodeling-Based Optimization (2014, methodology): “Methods include the least squares estimator [39, 22, 34, 47, 29, 75, 24, 27], order restricted splines [71, 48, 49, 65], constrained kernel regression [11], and Bernstein polynomials [18].”