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A J-Function for Marked Point Patterns

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Abstract

We propose a new summary statistic for marked point patterns. The underlying principle is to compare the distance from a marked point to the nearest other marked point in the pattern to the same distance seen from an arbitrary point in space. Information about the range of interaction can be inferred, and the statistic is well-behaved under random mark allocation. We develop a range of Hanisch style kernel estimators to tackle the problems of exploding tail variance earlier associated with J-function plug-in estimators, and carry out an exploratory analysis of a forestry data set.

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Authors and Affiliations

  1. Department PNA4, Centrum voor Wiskunde en Informatica, P.O. Box 94079, 1090, GB, Amsterdam, The Netherlands

    M. N. M. van Lieshout

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  1. M. N. M. van Lieshout
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Correspondence to M. N. M. van Lieshout.

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Lieshout, M.N.M.v. A J-Function for Marked Point Patterns. Ann Inst Stat Math 58, 235–259 (2006). https://doi.org/10.1007/s10463-005-0015-7

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  • DOI: https://doi.org/10.1007/s10463-005-0015-7

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