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{1078951125,
author = {Hall, Peter and Melville, Gavin and Welsh, Alan H.},
title = {Bias correction and bootstrap methods for a spatial sampling scheme},
journal = {Bernoulli},
volume = {7},
number = {6},
year = {2001},
pages = { 829-846},
language = {en},
url = {http://dml.mathdoc.fr/item/1078951125}
}
Hall, Peter; Melville, Gavin; Welsh, Alan H. Bias correction and bootstrap methods for a spatial sampling scheme. Bernoulli, Tome 7 (2001) no. 6, pp. 829-846. http://gdmltest.u-ga.fr/item/1078951125/