A consistent nonparametric estimation of spatial autocovariances

We examine some aspects of estimating sample autocovariances for spatial processes. Especially, we note that for such processes, it is not possible to approximate the expectation by the sample mean, like in the case of time series data. Then, we propose a consistent nonparametric estimation of sample autocovariances for an irregularly scattered spatial process, derived from a transformation of the initial process. We also suggest an L_2-consistent weighting matrix. Monte Carlo simulations are used to evaluate the performance of the proposed estimators in finite samples.