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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Description/Abstract
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 |
| Item ID: | 29939 |
| Date Deposited: | 11 May 2006 |
| Last Modified: | 01 Jun 2011 16:33 |
| Contributors: | Hall, Peter (Author) Melville, Gavin (Author) Welsh, Alan H. (Author) |
| Date: | 2001 |
| Status: | Published |
| Contact Email Address: | halpstat@fac.anu.edu.au |
| URI: | http://eprints.soton.ac.uk/id/eprint/29939 |
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