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December 2001 Bias correction and bootstrap methods for a spatial sampling scheme
Peter Hall, Gavin Melville, Alan H. Welsh
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Bernoulli 7(6): 829-846 (December 2001).

Abstract

Motivated by sampling problems in forestry and related fields, we suggest a spatial sampling scheme for estimating the intensity of a point process. The technique is related to the `wandering quarter' method. In applications where the cost of identifying random points is high relative to the cost of taking measurements, for example when identification involves travelling within a large region, our approach has significant advantages over more traditional approaches such as T-square sampling. When the point process is Poisson we suggest a simple bias correction for a `naive' estimator of intensity, and also discuss a more complex estimator based on maximum likelihood. A technique for pivoting, founded on a fourth-root transformation, is proposed and shown to yield second-order accuracy when applied to construct bootstrap confidence intervals for intensity. Bootstrap methods for correcting edge effects and for addressing non-Poisson point-process models are also suggested.

Citation

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Peter Hall. Gavin Melville. Alan H. Welsh. "Bias correction and bootstrap methods for a spatial sampling scheme." Bernoulli 7 (6) 829 - 846, December 2001.

Information

Published: December 2001
First available in Project Euclid: 10 March 2004

zbMATH: 0996.62089
MathSciNet: MR1873831

Keywords: Boundary effect , Confidence interval , edge effect , forestry , intensity estimation , pivotal statistic , Poisson process , T-square sampling , wandering quarter sampling

Rights: Copyright © 2001 Bernoulli Society for Mathematical Statistics and Probability

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Vol.7 • No. 6 • December 2001
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