On the functional local linear estimate for spatial regression

Abstract Consider Z i  = ( X i , Y i ), i  ∈ ℤ N be an F×ℝ-valued measurable strictly stationary spatial process, where F is a semi-metric space. We study the spatial covariation between X i and Y i by using the local linear estimate of the functional spatial regression E[ Y i | X i ]. The main result of this work is the establishment of the almost complete convergence for the proposed estimator, under some general conditions. We illustrate our methodology by applying the estimator to climatological data.