A Note on Exponential Inequalities in Hilbert Spaces for Spatial Processes with Applications to the Functional Kernel Regression Model
Statistics Theory
2017-11-15 v2 Statistics Theory
Abstract
In this manuscript we present exponential inequalities for spatial lattice processes which take values in a separable Hilbert space and satisfy certain dependence conditions. We consider two types of dependence: spatial data under -mixing conditions and spatial data which satisfies a weak dependence condition introduced by Dedecker and Prieur [2005]. We demonstrate their usefulness in the functional kernel regression model of Ferraty and Vieu [2004] where we study uniform consistency properties of the estimated regression operator on increasing subsets of the underlying function space.
Cite
@article{arxiv.1708.08505,
title = {A Note on Exponential Inequalities in Hilbert Spaces for Spatial Processes with Applications to the Functional Kernel Regression Model},
author = {Johannes T. N. Krebs},
journal= {arXiv preprint arXiv:1708.08505},
year = {2017}
}