On optimal spatial subsample size for variance estimation

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dc.creatorNordman, Daniel J.
dc.creatorLahiri, Soumendra N.
dc.date2005-03-29
dc.date.accessioned2026-07-07T08:06:46Z
dc.date.available2026-07-07T08:06:46Z
dc.descriptionWe 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.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053604000000779 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0503671
dc.identifierhttp://arxiv.org/abs/math/0503671
dc.identifierAnnals of Statistics 2004, Vol. 32, No. 5, 1981-2027
dc.identifierdoi:10.1214/009053604000000779
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130719
dc.subjectStatistics Theory
dc.subject62G09 (Primary) 62M40, 60G60. (Secondary)
dc.titleOn optimal spatial subsample size for variance estimation
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