Title: A Note on Exponential Inequalities in Hilbert Spaces for Spatial Processes with Applications to the Functional Kernel Regression Model,
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
$\alpha$-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.