On nonparametric variance estimation for second-order statistics of inhomogeneous spatial point processes with a known parametric intensity form

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Abstract

We introduce new variance estimation procedures for second-order statistics that are computed from a single realization of intensity reweighted stationary spatial point processes. The statistics are defined either on a subset B of the observation window or on the whole window. For the former, we use subblocks that have the same size and shape as B as "replicates" of B in order to estimate the target variance. For the latter, we develop a subsampling estimator for a key component in the target variance and estimate its other components by method-of-moment methods. Under some suitable conditions, we prove that the proposed variance estimators are consistent for the target variances in both cases. Simulations and an application to a real data example are used to demonstrate the usefulness of the proposed methods. This article has supplementary material online.

Original languageEnglish (US)
Pages (from-to)1482-1491
Number of pages10
JournalJournal of the American Statistical Association
Volume104
Issue number488
DOIs
StatePublished - Dec 1 2009
Externally publishedYes

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Keywords

  • Intensity reweighted stationary processes
  • Second-order statistics
  • Variance estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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