  We study a nonparametric regression model for sample data which is defined on
an $N$-dimensional lattice structure and which is assumed to be strong spatial
mixing: we use design adapted multidimensional Haar wavelets which form an
orthonormal system w.r.t. the empirical measure of the sample data. For such
orthonormal systems, we consider a nonparametric hard thresholding estimator.
We give sufficient criteria for the consistency of this estimator and we derive
rates of convergence. The theorems reveal that our estimator is able to adapt
to the local smoothness of the underlying regression function and the design
distribution. We illustrate our results with simulated examples.
