Non‐parametric regression with wavelet kernels

Applied Stochastic Models in Business and Industry (Impact Factor: 0.53). 03/2005; 21(2):153 - 163. DOI: 10.1002/asmb.533

ABSTRACT 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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