Bias correction and bootstrap methods for a spatial sampling scheme

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


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Motivated by sampling problems in forestry and related fields, we suggest a spatial sampling scheme for estimating 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.

Item Type: Article
ISSNs: 1350-7265 (print)
Related URLs:
Keywords: boundary effect, confidence interval, edge effect, forestry, intensity estimation, pivotal statistic, Poisson process, T-square sampling, wandering quarter sampling
Subjects: Q Science > QA Mathematics
S Agriculture > SD Forestry
H Social Sciences > HA Statistics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Statistics
ePrint ID: 29939
Accepted Date and Publication Date:
Date Deposited: 11 May 2006
Last Modified: 31 Mar 2016 11:56

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