Inference for spatial processes using subsampling: A simulation study

Many environmental studies involve the measurement of ecological indices that yield spatially dependent data. One quantity that captures the empirical distribution of ecological measurements is the spatial cumulative distribution function (SCDF). Methods for making inferential statements about SCDFs have only recently been developed, one being that of spatial subsampling. While spatial subsampling produces inferential quantities with known asymptotic properties, the performance of this methodology in a finite-sample setting has not previously been investigated. In this article, we review the subsampling method and its theoretical justification, and investigate the performance of this method for finite samples with a simulation study involving several subsampling designs and types of spatial dependence. The subsampling methodology appears to give quite good results over a range of realistic spatial processes. For application to a set of spatially dependent data, an appropriate subsampling procedure may be designed on the basis of quantities contained in the (estimated) variogram.