On optimal spatial subsample size for variance estimation

Details On optimal spatial subsample size for variance estimation On optimal spatial subsample size for variance estimation

2005-03-29

arxiv.org/abs/math/0503671v1

Annals of Statistics 2004, Vol. 32, No. 5, 1981-2027

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000779 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000000779

We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance estimator, which yields an expression for the theoretically optimal block size. The optimal block size is shown to depend in an intricate way on the geometry of the spatial sampling region as well as characteristics of the underlying random field. Final expressions for the optimal block size make use of some nontrivial estimates of lattice point counts in shifts of convex sets. Optimal block sizes are computed for sampling regions of a number of commonly encountered shapes. Numerical studies are performed to compare subsampling methods as well as procedures for estimating the theoretically best block size.

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