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December 1995 Locally lattice sampling designs for isotropic random fields
Michael L. Stein
Ann. Statist. 23(6): 1991-2012 (December 1995). DOI: 10.1214/aos/1034713644


For predicting $\int_G v(x)Z(x)dx$, where v is a fixed known function and Z is a stationary random field, a good sampling fesign should have a greater density of observations where v is relatively large in absolute value. Designs using this idea when $G = [0, 1]$ have been studied for some time. For G a region in two dimensions, very little is known about the statistical properties of cubature rules based on designs with varying density. This work proposes a class of designs that are locally parallelogram lattices but whose densities can vary. The asymptotic variance of the cubature error for these designs is obtained for a class of isotropic random fields and an asymptotically optimal sequence of cubature rules within this class is found. I conjecture that this sequence of cubature rules is asymptotically optimal with respect to all cubature rules.


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Michael L. Stein. "Locally lattice sampling designs for isotropic random fields." Ann. Statist. 23 (6) 1991 - 2012, December 1995.


Published: December 1995
First available in Project Euclid: 15 October 2002

zbMATH: 0856.62084
MathSciNet: MR1389862
Digital Object Identifier: 10.1214/aos/1034713644

Primary: 62M40
Secondary: 65D32

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 6 • December 1995
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