On the estimation of the distribution of sample means based on non-stationary spatial data

Two different methods of estimating the distribution of sample means based on non-stationary spatially indexed data {Xi : i E I}, where I is a finite subset of the integer lattice 71}, are presented. The information in the different cells in the lattice are allowed to come from different distributions, but with the same expected value or with expected values that can be decomposed additively into directional components. Furthermore, neighboring lattice cells are assumed to be dependent, and the dependence structure is allowed to differ over the lattice. It will be shown under such rather general conditions that the distribution of the sample mean can be estimated by resampling, as well as by a normal approximation for which a non-parametric estimator of variance is provided. The developed methods can be applied in assessing accuracy of statistical inference for spatial data. Key words: resampling, m-dependent random variables, estimating distributions, spatial data on integer lattices.

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