Kernel regression estimation for continuous spatial processes

We investigate here a kernel estimate of the spatial regression function r(x) = E(Y ^sub u^ | X ^sub u^ = x), x ^sup d^ , of a stationary multidimensional spatial process { Z ^sub u^ = (X ^sub u^ , Y ^sub u^ ), u ^sup N^ }. The weak and strong consistency of the estimate is shown under sufficient conditions on the mixing coefficients and the bandwidth, when the process is observed over a rectangular domain of ^sup N^ . Special attention is paid to achieve optimal and suroptimal strong rates of convergence. It is also shown that this suroptimal rate is preserved by using a suitable spatial sampling scheme.[PUBLICATION ABSTRACT]