On optimal spatial subsample size for variance estimation

Daniel J. Nordman; Soumendra N. Lahiri

In this paper, we consider the problem of determining the optimal block 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 theoretical optimal block size. The theoretical optimal block size is shown to depend in an intricate way on the geometry of the spatial sampling region as well as on the 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. Examples are presented to illustrate the variations in optimal block size for sampling regions of different shapes.

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Year of publication:	2002
Authors:	Nordman, Daniel J. ; Lahiri, Soumendra N.
Publisher:	Dortmund : SFB 475, Universität Dortmund
Subject:	Block bootstrap \| block size \| lattice point count \| mixing \| nonparametric variance \| estimation \| random fields \| spatial statistics \| subsampling method \| Schätztheorie \| Estimation theory \| Bootstrap-Verfahren \| Bootstrap approach \| Stichprobenerhebung \| Sampling \| Nichtparametrisches Verfahren \| Nonparametric statistics