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FREE-KNOT SPLINES AND ADAPTIVE KNOT SELECTION
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BibTeX
@MISC{Miyata_free-knotsplines,
author = {Satoshi Miyata and Xiaotong Shen},
title = {FREE-KNOT SPLINES AND ADAPTIVE KNOT SELECTION},
year = {}
}
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Abstract
Conventional spline procedures have proven to be effective and useful for estimat-ing smooth functions. However, these procedures find piecewise and inhomogeneous smooth functions difficult to handle. Conventional spline procedures often yield an overly-smooth curve in regions where the true function or its derivative are discon-tinuous. To fully realize the potential of the spline methodology, this article proposes a function estimation procedure that uses adaptive free-knot splines and allows for multiple knots to be replaced at the same location and between design points. The article also proposes an associated algorithm for implementation in non-parametric regression. The proposed knot selection scheme uses a data-adaptive model selec-tion criterion and an evolutionary algorithm that incorporates certain key features of simulated annealing. The evolutionary algorithm accurately locates the optimal knots, while the data-driven penalty guards against selection errors when searching through a large candidate knot space. The algorithm stochastically yields the globally optimal knots. The simulations suggest that the procedure performs competitively well against alternative methods and has a substantial advantage in relation to non-smooth and piecewise smooth functions. Key words and phrases: Adaptive model selection, evolutionary algorithms, inhomo-geneous smoothness, non-parametric regression, signal processing, spatial adaptation, variable multiple knots. 1.
Keyphrases
free-knot spline adaptive knot selection evolutionary algorithm optimal knot non-parametric regression conventional spline procedure large candidate knot space simulated annealing multiple knot signal processing smooth function selection error true function function estimation procedure data-adaptive model selec-tion criterion key word estimat-ing smooth function adaptive model selection inhomogeneous smooth function spatial adaptation design point substantial advantage alternative method adaptive free-knot spline certain key feature overly-smooth curve spline methodology inhomo-geneous smoothness associated algorithm variable multiple knot knot selection scheme data-driven penalty guard
