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Moment estimation for statistics from marked point processes

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  • Dimitris N. Politis
  • Michael Sherman

Abstract

In spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations; in other words, the data form a realization of a marked point process. In this paper, we formulate subsampling estimators of the moments of general statistics computed from marked point process data, and we establish their L2‐consistency. The variance estimator in particular can be used for the construction of confidence intervals for estimated parameters. A practical data‐based method for choosing a subsampling parameter is given and illustrated on a data set. Finite sample simulation examples are also presented.

Suggested Citation

  • Dimitris N. Politis & Michael Sherman, 2001. "Moment estimation for statistics from marked point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 261-275.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:2:p:261-275
    DOI: 10.1111/1467-9868.00284
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    Cited by:

    1. Michaela Prokešová & Eva Jensen, 2013. "Asymptotic Palm likelihood theory for stationary point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 387-412, April.
    2. Yongtao Guan & Michael Sherman & James A. Calvin, 2006. "Assessing Isotropy for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 62(1), pages 119-125, March.
    3. Xianyang Zhang & Bo Li & Xiaofeng Shao, 2014. "Self-normalization for Spatial Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 311-324, June.
    4. Yongtao Guan, 2008. "A KPSS Test for Stationarity for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 64(3), pages 800-806, September.
    5. Yongtao Guan, 2006. "Tests for Independence between Marks and Points of a Marked Point Process," Biometrics, The International Biometric Society, vol. 62(1), pages 126-134, March.
    6. Yongtao Guan, 2011. "Bias-Corrected Variance Estimation and Hypothesis Testing for Spatial Point and Marked Point Processes Using Subsampling," Biometrics, The International Biometric Society, vol. 67(3), pages 926-936, September.
    7. Lothar Heinrich & Michaela Prokešová, 2010. "On Estimating the Asymptotic Variance of Stationary Point Processes," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 451-471, September.
    8. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Srijan Sengupta & Xiaofeng Shao & Yingchuan Wang, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 315-326, May.

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