Resumen
Consider a stationary random field {X"n} indexed by N-dimensional lattice points, where {X"n} takes values in R^d. An important problem in spatial statistics is the estimation of the regression of {X"n} on the values of the random field at surrounding sites, say, X"n"""1,...,X"n"""@?. Note that (X"n"""1,...,X"n"""@?) is a @?d-dimensional vector. Assume the existence of the regression function r(x)=E{@f(X"n)|(X"n"""1,...,X"n"""@?)=x},where @f is a continuous real-valued function which is not necessarily bounded, and x@?R^@?^d. Kernel-type estimators of the regression function r(x) are investigated. They are shown to converge uniformly on compact sets under general conditions. In addition, they can attain the optimal rates of convergence in L"~. The results hold for a large class of spatial processes.