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

Research output: Contribution to journalArticle

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 2011
Externally publishedYes

Fingerprint

Marked Point Process
Subsampling
Variance Estimation
Hypothesis Testing
Extrapolation
Variance Estimator
Statistics
Test Statistic
Testing
Covariance matrix
Regression
Bias Correction
Optimal Rates
statistics
testing
Observation
Mean Squared Error
Linear Combination
tropical forests
Estimator

Keywords

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

ASJC Scopus subject areas

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

Cite this

Bias-Corrected Variance Estimation and Hypothesis Testing for Spatial Point and Marked Point Processes Using Subsampling. / Guan, Yongtao.

In: Biometrics, Vol. 67, No. 3, 09.2011, p. 926-936.

Research output: Contribution to journalArticle

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