Non-parametric Regression for Spatially Dependent Data with Wavelets

TL;DR

This paper develops non-parametric regression methods for spatially dependent data on lattices, using wavelets, and establishes their consistency, convergence rates, and practical estimation via simulations on planar graphs.

Contribution

It introduces wavelet-based non-parametric regression for spatial data with strong mixing conditions, providing theoretical guarantees and practical algorithms.

Findings

Consistency and optimal convergence rates of the estimators.

Effective wavelet-based estimation for multidimensional spatial data.

Successful simulation studies on planar graphs demonstrating the method.

Abstract

We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular $N$-dimensional lattice structure. We show consistency and obtain rates of convergence. The rates are optimal modulo a logarithmic factor in some cases. As an application, we estimate the regression function with multidimensional wavelets which are not necessarily isotropic. We simulate random fields on planar graphs with the concept of concliques (cf. Kaiser et al. [2012]) in numerical examples of the estimation procedure.