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Title: Kernel partial least squares for stationary data Authors:  Marco Singer - Georg-August-Universitaet Goettingen (Germany) [presenting]
Tatyana Krivobokova - Georg-August-Universitaet Goettingen (Germany)
Axel Munk - Georg-August-University Goettingen (Germany)
Abstract: The kernel partial least squares algorithm for nonparametric regression with stationary dependent data is considered. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are established when the algorithm is stopped early. The convergence rates depend on three quantities: the regularity of the target function given by a source condition, the effective dimensionality of the data mapped into the reproducing kernel Hilbert space and the the range of dependence in the data measured via the polynomial decay of the autocovariance function. It is shown both theoretically and in simulations that long range dependence results in slower convergence rates.