Nonparametric Linear Regression for Spatial Data on Graphs with Wavelets

Nonparametric regression estimates for $d$-dimensional random fields are studied. The data is defined on a not necessarily regular $N$-dimensional lattice structure and is strong mixing. We show the consistency and obtain rates of convergence for nonparametric regression estimators which are derived from finite dimensional linear function spaces. As an application, we estimate the regression function with $d$-dimensional wavelets which are not necessarily isotropic. We give numerical examples of the estimation procedure where we simulate random fields on planar graphs with the concept of concliques (Kaiser [2012]).