• Bernoulli
  • Volume 7, Number 6 (2001), 829-846.

Bias correction and bootstrap methods for a spatial sampling scheme

Peter Hall, Gavin Melville, and Alan H. Welsh

Full-text: Open access


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.

Article information

Bernoulli, Volume 7, Number 6 (2001), 829-846.

First available in Project Euclid: 10 March 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

boundary effect confidence interval edge effect forestry intensity estimation pivotal statistic Poisson process T-square sampling wandering quarter sampling


Hall, Peter; Melville, Gavin; Welsh, Alan H. Bias correction and bootstrap methods for a spatial sampling scheme. Bernoulli 7 (2001), no. 6, 829--846.

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