The Annals of Statistics

On optimal spatial subsample size for variance estimation

Daniel J. Nordman and Soumendra N. Lahiri

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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.

Article information

Ann. Statist., Volume 32, Number 5 (2004), 1981-2027.

First available in Project Euclid: 27 October 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G09: Resampling methods
Secondary: 62M40: Random fields; image analysis 60G60: Random fields

Block bootstrap block size lattice point count nonparametric variance estimation random fields spatial statistics subsampling method


Nordman, Daniel J.; Lahiri, Soumendra N. On optimal spatial subsample size for variance estimation. Ann. Statist. 32 (2004), no. 5, 1981--2027. doi:10.1214/009053604000000779.

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