Non‐parametric regression with wavelet kernels | Zendy

Rakotomamonjy Alain | Zendy; Mary Xavier | Zendy; Canu Stéphane | Zendy

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Non‐parametric regression with wavelet kernels

Author(s) -

Rakotomamonjy Alain,

Mary Xavier,

Canu Stéphane

Publication year - 2005

Publication title -

applied stochastic models in business and industry

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.413

H-Index - 40

eISSN - 1526-4025

pISSN - 1524-1904

DOI - 10.1002/asmb.533

Subject(s) - wavelet , kernel (algebra) , mathematics , parametric statistics , kernel regression , representer theorem , hilbert space , nonparametric regression , computer science , kernel method , artificial intelligence , set (abstract data type) , reproducing kernel hilbert space , algorithm , regression , mathematical optimization , pattern recognition (psychology) , kernel embedding of distributions , statistics , discrete mathematics , pure mathematics , support vector machine , programming language

This paper introduces a method to construct a reproducing wavelet kernel Hilbert spaces for non‐parametric regression estimation when the sampling points are not equally spaced. Another objective is to make high‐dimensional wavelet estimation problems tractable. It then provides a theoretical foundation to build reproducing kernel from operators and a practical technique to obtain reproducing kernel Hilbert spaces spanned by a set of wavelets. A multiscale approximation technique that aims at taking advantage of the multiresolution structure of wavelets is also described. Examples on toy regression and a real‐world problem illustrate the effectiveness of these wavelet kernels. Copyright © 2005 John Wiley & Sons, Ltd.

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