A thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns

Yongtao Guan, Ji Meng Loh

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

When modeling inhomogeneous spatial point patterns, it is of interest to fit a parametric model for the first-order intensity function (FOIF) of the process in terms of some measured covariates. Estimates for the regression coefficients, say β, can be obtained by maximizing a Poisson maximum likelihood criterion. Little work has been done on the asymptotic distribution of β except in some special cases. In this article we show that β is asymptotically normal for a general class of mixing processes. To estimate the variance of β, we propose a novel thinned block bootstrap procedure that assumes that the point process is second-order reweighted stationary. To apply this procedure, only the FOIF, and not any high-order terms of the process, needs to be estimated. We establish the consistency of the resulting variance estimator, and demonstrate its efficacy through simulations and an application to a real data example.

Original languageEnglish (US)
Pages (from-to)1377-1386
Number of pages10
JournalJournal of the American Statistical Association
Volume102
Issue number480
DOIs
StatePublished - Dec 1 2007
Externally publishedYes

Keywords

  • Block bootstrap
  • Inhomogeneous spatial point process
  • Thinning

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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