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October 2004 On optimal spatial subsample size for variance estimation
Daniel J. Nordman, Soumendra N. Lahiri
Ann. Statist. 32(5): 1981-2027 (October 2004). DOI: 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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Daniel J. Nordman. Soumendra N. Lahiri. "On optimal spatial subsample size for variance estimation." Ann. Statist. 32 (5) 1981 - 2027, October 2004.


Published: October 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1056.62055
MathSciNet: MR2102500
Digital Object Identifier: 10.1214/009053604000000779

Primary: 62G09
Secondary: 60G60 , 62M40

Keywords: block bootstrap , block size , lattice point count , nonparametric variance estimation , Random fields , spatial statistics , subsampling method

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 5 • October 2004
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