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.
|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
|Accepted Date and Publication Date:||
|Date Deposited:||11 May 2006|
|Last Modified:||31 Mar 2016 11:56|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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