Nonparametric Linear Regression for Spatial Data on Graphs with Wavelets

Nonparametric regression estimates for $d$-dimensional data are studied. The data is defined on a not necessarily regular $N$-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 $d$-dimensional wavelets. Furthermore, we give numerical applications of the developed theory.