Density estimation for spatial linear processes

The problem of estimating the marginal densities of a spatial linear proces s, observed over a grid of Z(N), is considered. Under general conditions, k ernel density estimators computed at any k-tuple of sites are shown to be a symptotically multivariate normal. Their limiting covariance matrix is also computed. Despite the huge development of nonparametric estimation methods in the analysis of time series data, little has so far been done to introd uce them into the context of random fields. The generalization is far from trivial since the points of Z(N) do not have a natural ordering when N>1. N o mixing conditions are required, but linearity is assumed.