The Annals of Statistics

On optimal spatial subsample size for variance estimation

Daniel J. Nordman and Soumendra N. Lahiri

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Abstract

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

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

Dates
First available in Project Euclid: 27 October 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1098883779

Digital Object Identifier
doi:10.1214/009053604000000779

Mathematical Reviews number (MathSciNet)
MR2102500

Zentralblatt MATH identifier
1056.62055

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1098883779


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