A Note on Exponential Inequalities in Hilbert Spaces for Spatial Processes with Applications to the Functional Kernel Regression Model
  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.
