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Nonparametric Linear Regression for Spatial Data on Graphs with Wavelets

Abstract

Nonparametric regression estimates for dd-dimensional data are studied. The data is defined on a not necessarily regular NN-dimensional lattice structure and is strong mixing. We show the consistency and get rates of convergence for nonparametric regression estimators which are derived from finite dimensional linear function spaces. As an application, we choose linear spaces which are spanned by dd-dimensional wavelets. Furthermore, we give numerical applications of the developed theory.

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