Estimation of the variance of sample means based on nonstationary spatial data with varying expected values

Subsampling and block resampling methods have been suggested in the literature to nonparametrically estimate the variance of some statistic computed from spatial data. Usually stationary data are required. However, in empirical applications, the assump­ tion of stationarity can often be rejected. This paper proposes nonparametric methods to estimate the variance of sample means based on nonstationary spatial data using subsam­ pling. It is assumed that data is observed on a rectangular lattice in some subregion of R 2. The kind of data we consider is of the following type: The information in the different picture elements (pixels) of the lattice are allowed to come from different distributions, with smoothly varying expected values, or with expected values decomposed additively into directional components. Furthermore, pixels are assumed to be locally dependent, and the dependence structure is allowed to differ over the lattice. Consistent variance esti­ mators for sample means, and convergence rates in mean square, are provided under these assumptions. An example with applications to forestry, using satellite data, is discussed.