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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Vydáno v:Computational statistics & data analysis Ročník 45; číslo 2; s. 159 - 178
Hlavní autoři: Molinari, Nicolas, Durand, Jean-François, Sabatier, Robert
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 01.03.2004
Elsevier Science
Elsevier
Edice:Computational Statistics & Data Analysis
Témata:
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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Popis
Shrnutí: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.
ISSN:0167-9473
1872-7352
DOI:10.1016/S0167-9473(02)00343-2