Non-parametric regression with wavelet kernels

This paper introduces a method to construct a reproducing wavelet kernel Hilbert spaces for nonparametric 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 (c) 2005 John Wiley & Sons, Ltd.