On optimal spatial subsample size for variance estimation. (English) Zbl 1056.62055

Nordman, Daniel J.; Lahiri, Soumendra N.

Ann. Stat. 32, No. 5, 1981-2027 (2004).

Summary: 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 is 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.

MSC:

62G09	Nonparametric statistical resampling methods
62M30	Inference from spatial processes
62M40	Random fields; image analysis
60G60	Random fields

Keywords:

block bootstrap; block size; lattice point count; variance estimation; spatial statistics; subsampling method

Software:

AS 312; spatial

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