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On the Estimation of Integrated Covariance Functions of Stationary Random Fields

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  • URSA PANTLE
  • VOLKER SCHMIDT
  • EVGENY SPODAREV

Abstract

. For stationary vector‐valued random fields on the asymptotic covariance matrix for estimators of the mean vector can be given by integrated covariance functions. To construct asymptotic confidence intervals and significance tests for the mean vector, non‐parametric estimators of these integrated covariance functions are required. Integrability conditions are derived under which the estimators of the covariance matrix are mean‐square consistent. For random fields induced by stationary Boolean models with convex grains, these conditions are expressed by sufficient assumptions on the grain distribution. Performance issues are discussed by means of numerical examples for Gaussian random fields and the intrinsic volume densities of planar Boolean models with uniformly bounded grains.

Suggested Citation

  • Ursa Pantle & Volker Schmidt & Evgeny Spodarev, 2010. "On the Estimation of Integrated Covariance Functions of Stationary Random Fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 47-66, March.
    • Handle: RePEc:bla:scjsta:v:37:y:2010:i:1:p:47-66
    DOI: 10.1111/j.1467-9469.2009.00663.x
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    References listed on IDEAS

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    1. Schmidt, Volker & Spodarev, Evgueni, 2005. "Joint estimators for the specific intrinsic volumes of stationary random sets," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 959-981, June.
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    Cited by:

    1. Wang, Jiangyan & Cao, Guanqun & Wang, Li & Yang, Lijian, 2020. "Simultaneous confidence band for stationary covariance function of dense functional data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    2. Elena Di Bernardino & Céline Duval, 2022. "Statistics for Gaussian random fields with unknown location and scale using Lipschitz‐Killing curvatures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 143-184, March.

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