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Optimal sampling designs for nonparametric estimation of spatial averages of random fields


  • Benhenni, Karim
  • Su, Yingcai


Optimal designs of sampling spatial locations in estimating spatial averages of random fields are considered. The random field is assumed to have correlated values according to a covariance function. The quality of estimation is measured by the mean squared error. Simple nonparametric linear estimators along with sampling designs having a limiting density are considered. For a large class of locally isotropic random fields, we argue for the asymptotic optimality of simple linear estimators. The convergent rates of the mean squared error and optimal limiting densities of sampling designs are determined in every dimension. An example of simulation is given.

Suggested Citation

  • Benhenni, Karim & Su, Yingcai, 2016. "Optimal sampling designs for nonparametric estimation of spatial averages of random fields," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 341-351.
  • Handle: RePEc:eee:jmvana:v:146:y:2016:i:c:p:341-351
    DOI: 10.1016/j.jmva.2015.11.010

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    References listed on IDEAS

    1. Robinson, P.M., 2011. "Asymptotic theory for nonparametric regression with spatial data," Journal of Econometrics, Elsevier, vol. 165(1), pages 5-19.
    2. Gérard Biau & Benoît Cadre, 2004. "Nonparametric Spatial Prediction," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 327-349, October.
    3. Nerini, David & Monestiez, Pascal & Manté, Claude, 2010. "Cokriging for spatial functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 409-418, February.
    4. Su, Yingcai & Cambanis, Stamatis, 1993. "Sampling designs for estimation of a random process," Stochastic Processes and their Applications, Elsevier, vol. 46(1), pages 47-89, May.
    5. Peter Robinson, 2011. "Asymptotic theory for nonparametric regression with spatial data," CeMMAP working papers CWP11/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Marc Hallin & Zudi Lu & Lanh T. Tran, 2004. "Local linear spatial regression," ULB Institutional Repository 2013/2131, ULB -- Universite Libre de Bruxelles.
    7. Su, Yingcai, 1997. "Estimation of random fields by piecewise constant estimators," Stochastic Processes and their Applications, Elsevier, vol. 71(2), pages 145-163, November.
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