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Nonparametric Linear Regression for Spatial Data on Graphs with Wavelets

21 September 2016
Johannes T. N. Krebs
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Abstract

Nonparametric regression estimates for ddd-dimensional random fields are studied. The data is defined on a not necessarily regular NNN-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 ddd-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]).

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