Statistics and Its Interface

Volume 5 (2012)

Number 2

Nonparametric estimation of the dependence of a spatial point process on spatial covariates

Pages: 221 – 236

DOI: http://dx.doi.org/10.4310/SII.2012.v5.n2.a7

Authors

Adrian Baddeley (CSIRO Mathematics, Informatics and Statistics, Floreat, Perth, Western Australia)

Ya-Mei Chang (Department of Statistics, Tamkang University, Taiwan)

Yong Song (CSIRO Land and Water Highett, Melbourne, Australia)

Rolf Turner (Department of Statistics, University of Auckland, New Zealand)

Abstract

In the statistical analysis of spatial point patterns, it is often important to investigate whether the point pattern depends on spatial covariates. This paper describes nonparametric (kernel and local likelihood) methods for estimating the effect of spatial covariates on the point process intensity. Variance estimates and confidence intervals are provided in the case of a Poisson point process. Techniques are demonstrated with simulated examples and with applications to exploration geology and forest ecology.

Keywords

confidence intervals, density estimation, kernel smoothing, local likelihood, logistic regression, point process intensity, poisson point process, [geological] prospectivity mapping, spatial covariates, relative distributions, resource selection function, weighted distribution

2010 Mathematics Subject Classification

Primary 62G07, 62H11. Secondary 62M30.

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