On asymptotic properties of the mark variogram estimator of a marked point process

Yongtao Guan, Michael Sherman, James A. Calvin

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

The mark variogram [Cressie, 1993. Statistics for Spatial Data. Wiley, New York] is a useful tool to analyze data from marked point processes. In this paper, we investigate the asymptotic properties of its estimator. Our main findings are that the sample mark variogram is a consistent estimator for the true mark variogram and is asymptotically normal under some mild conditions. These results hold for both the geostatistical marking case (i.e., the case where the marks and points are independent) and the non-geostatistical marking case (i.e., the case where the marks and points are dependent). As an application we develop a general test for spatial isotropy and study our methodology through a simulation study and an application to a data set on long leaf pine trees.

Original languageEnglish (US)
Pages (from-to)148-161
Number of pages14
JournalJournal of Statistical Planning and Inference
Volume137
Issue number1
DOIs
StatePublished - Jan 1 2007

Keywords

  • Mark variogram
  • Marked point process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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