Bounded optimal knots for regression splines

Using a B-spline representation for splines with knots seen as free variables, the approximation to data by splines improves greatly. The main limitations are the presence of too many local optima in the univariate regression context, and it becomes even worse in multivariate additive modeling. When...

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Vydané v:	Computational statistics & data analysis Ročník 45; číslo 2; s. 159 - 178
Hlavní autori:	Molinari, Nicolas, Durand, Jean-François, Sabatier, Robert
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 01.03.2004 Elsevier Science Elsevier
Edícia:	Computational Statistics & Data Analysis
Predmet:	Additive models AIC BIC Bound constrained optimization Exact sciences and technology Free knots selection Linear inference, regression Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Probability and statistics Sciences and techniques of general use Statistics Surface estimation Free knots selection Surface estimation AIC Bound constrained optimization BIC Additive models B spline Statistical method Free knot selection Additive process Least squares method Regression spline AIC and BIC Spline approximation Constrained optimization
ISSN:	0167-9473, 1872-7352
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Abstract	Using a B-spline representation for splines with knots seen as free variables, the approximation to data by splines improves greatly. The main limitations are the presence of too many local optima in the univariate regression context, and it becomes even worse in multivariate additive modeling. When the number of knots is a priori fixed, we present a simple algorithm to select their location subject to box constraints for computing least-squares spline approximations. Despite its simplicity, or perhaps because of it, the method is comparable with other more sophisticated techniques and is very attractive for a small number of variables, as shown in the examples. In a complete algorithm, the BIC and AIC criteria are evaluated for choosing the number of knots as well as the degree of the splines.
AbstractList	Using a B-spline representation for splines with knots seen as free variables, the approximation to data by splines improves greatly. The main limitations are the presence of too many local optima in the univariate regression context, and it becomes even worse in multivariate additive modeling. When the number of knots is a priori fixed, we present a simple algorithm to select their location subject to box constraints for computing least-squares spline approximations. Despite its simplicity, or perhaps because of it, the method is comparable with other more sophisticated techniques and is very attractive for a small number of variables, as shown in the examples. In a complete algorithm, the BIC and AIC criteria are evaluated for choosing the number of knots as well as the degree of the splines.
Author	Sabatier, Robert Durand, Jean-François Molinari, Nicolas
Author_xml	– sequence: 1 givenname: Nicolas surname: Molinari fullname: Molinari, Nicolas email: molinari@iurc.montp.inserm.fr organization: Laboratoire de Biostatistique, Institut Universitaire de Recherche Clinique, 641 avenue Gaston Giraud, 34093 Montpellier, France – sequence: 2 givenname: Jean-François surname: Durand fullname: Durand, Jean-François organization: Unit e de Biom e trie, ENSAM-INRA, 2, place Viala, 34060 Montpellier, France – sequence: 3 givenname: Robert surname: Sabatier fullname: Sabatier, Robert organization: Laboratoire de Physique Mol e culaire et Structurale, 15 av. Ch. Flahaut, 34060 Montpellier, France
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Cites_doi	10.1137/0710036 10.1016/0167-9473(93)90217-H 10.1145/356056.356066 10.1214/aos/1176344136 10.1214/aos/1031594728 10.2307/2284158 10.1111/1467-9868.00128 10.2307/1390640 10.1016/0304-4076(95)01763-1 10.1016/0021-9045(75)90056-8 10.1016/S0167-9473(99)00038-9 10.1007/BFb0099519 10.1214/aos/1176347969 10.1137/0715022 10.1007/BF02788653 10.1145/22899.22904 10.2307/1270359 10.1214/aos/1176347963 10.2307/2965423
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Keywords	Free knots selection Surface estimation AIC Bound constrained optimization BIC Additive models B spline Statistical method Free knot selection Additive process Least squares method Regression spline AIC and BIC Spline approximation Constrained optimization
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Amer. Statist. Assoc. doi: 10.2307/2965423
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Snippet	Using a B-spline representation for splines with knots seen as free variables, the approximation to data by splines improves greatly. The main limitations are...
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SubjectTerms	Additive models AIC BIC Bound constrained optimization Exact sciences and technology Free knots selection Linear inference, regression Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Probability and statistics Sciences and techniques of general use Statistics Surface estimation
Title	Bounded optimal knots for regression splines
URI	https://dx.doi.org/10.1016/S0167-9473(02)00343-2 http://econpapers.repec.org/article/eeecsdana/v_3a45_3ay_3a2004_3ai_3a2_3ap_3a159-178.htm
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