Abstract
We present a novel smoothing approach to nonparametric regression curve fitting.
This is based on kernel partial least squares (PLS) regression in reproducing kernel Hilbert space.
It is our interest to apply the methodology for smoothing experimental data, such as brain event related potentials, where some level of
knowledge about areas of different degrees of smoothness, local inhomogeneities or points where the desired function
changes its curvature is known or can be derived based on the observed noisy data.
With this aim we propose locally-based kernel PLS regression and locally-based smoothing splines methodologies
incorporating this knowledge. We illustrate the usefulness of kernel PLS and locally-based kernel PLS
smoothing by comparing the methods with smoothing splines, locally-based smoothing splines and wavelet shrinkage
techniques on two generated data sets. In terms of higher accuracy of the recovered signal of interest from its noisy observation
we demonstrate comparable or better performance of the locally-based kernel PLS method in comparison to other methods
on both data sets.
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