Bias-Corrected Variance Estimation and Hypothesis Testing for Spatial Point and Marked Point Processes Using Subsampling

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes. For variance estimation, our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval. We show that they can achieve better rates in mean squared error than the usual subsampling variance estimator. In particular, for n×n observation windows, the optimal rate ofn -2can be achieved if the data have a finite dependence range. For hypothesis testing, we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes, and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics. We assess the numerical performance of the proposed methods through simulation, and apply them to analyze a tropical forest data set.

Original languageEnglish (US)
Pages (from-to)926-936
Number of pages11
JournalBiometrics
Volume67
Issue number3
DOIs
StatePublished - Sep 1 2011
Externally publishedYes

Keywords

  • Bias correction
  • Spatial marked point process
  • Spatial point process
  • Subsampling

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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