  We propose to approximate the conditional expectation of a spatial random
variable given its nearest-neighbour observations by an additive function. The
setting is meaningful in practice and requires no unilateral ordering. It is
capable of catching nonlinear features in spatial data and exploring local
dependence structures. Our approach is different from both Markov field methods
and disjunctive kriging. The asymptotic properties of the additive estimators
have been established for $\alpha$-mixing spatial processes by extending the
theory of the backfitting procedure to the spatial case. This facilitates the
confidence intervals for the component functions, although the asymptotic
biases have to be estimated via (wild) bootstrap. Simulation results are
reported. Applications to real data illustrate that the improvement in
describing the data over the auto-normal scheme is significant when
nonlinearity or non-Gaussianity is pronounced.
