Kernel PLS Smoothing for Nonparametric Regression Curve Fitting: an Application to Event Related Potentials

We present a novel smoothing approach to nonparametric regression curve fltting. This isbasedonkernelpartialleastsquares(PLS)regressioninreproducingkernelHilbertspace. 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 difierent degrees of smoothness,localinhomogeneitiesorpointswherethedesiredfunctionchangesitscurvature isknownorcanbederivedbasedontheobservednoisydata. Withthisaimweproposelocally- basedkernelPLSregressionandlocally-basedsmoothingsplinesmethodologiesincorporating this knowledge. We illustrate the usefulness of kernel PLS and locally-based kernel PLS smoothingbycomparingthemethodswithsmoothingsplines,locally-basedsmoothingsplines 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 bothdatasets.