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

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8 Citations (Scopus)

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 2009
Externally publishedYes

Fingerprint

Spatial Point Process
Variance Estimation
Nonparametric Estimation
Order Statistics
Target
Subsampling
Moment Method
Variance Estimator
Method of Moments
Estimate
Statistics
Estimator
Subset
Demonstrate
Form
Order statistics
Point process
Variance estimation
Simulation

Keywords

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

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

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AB - 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.

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