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A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics

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  • Iranpanah, N.
  • Mohammadzadeh, M.
  • Taylor, C.C.

Abstract

Efron (1979) introduced the bootstrap method for independent data but it cannot be easily applied to spatial data because of their dependency. For spatial data that are correlated in terms of their locations in the underlying space the moving block bootstrap method is usually used to estimate the precision measures of the estimators. The precision of the moving block bootstrap estimators is related to the block size which is difficult to select. In the moving block bootstrap method also the variance estimator is underestimated. In this paper, first the semi-parametric bootstrap is used to estimate the precision measures of estimators in spatial data analysis. In the semi-parametric bootstrap method, we use the estimation of the spatial correlation structure. Then, we compare the semi-parametric bootstrap with a moving block bootstrap for variance estimation of estimators in a simulation study. Finally, we use the semi-parametric bootstrap to analyze the coal-ash data.

Suggested Citation

  • Iranpanah, N. & Mohammadzadeh, M. & Taylor, C.C., 2011. "A comparison of block and semi-parametric bootstrap methods for variance estimation in spatial statistics," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 578-587, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:578-587
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    References listed on IDEAS

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    1. Kent, J. T. & Mohammadzadeh, M., 1999. "Spectral Approximation to the Likelihood for an Intrinsic Gaussian Random Field," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 136-155, July.
    2. Politis, D. N. & Romano, J. P., 1993. "Nonparametric Resampling for Homogeneous Strong Mixing Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 301-328, November.
    3. Dale Zimmerman & Noel Cressie, 1992. "Mean squared prediction error in the spatial linear model with estimated covariance parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 27-43, March.
    4. Hall, Peter, 1985. "Resampling a coverage pattern," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 231-246, September.
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    Cited by:

    1. Hyunju Son & Youyi Fong, 2021. "Fast grid search and bootstrap‐based inference for continuous two‐phase polynomial regression models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    2. Castillo-Páez, Sergio & Fernández-Casal, Rubén & García-Soidán, Pilar, 2019. "A nonparametric bootstrap method for spatial data," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 1-15.
    3. Adler, Werner & Brenning, Alexander & Potapov, Sergej & Schmid, Matthias & Lausen, Berthold, 2011. "Ensemble classification of paired data," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1933-1941, May.
    4. Pigoli, Davide & Menafoglio, Alessandra & Secchi, Piercesare, 2016. "Kriging prediction for manifold-valued random fields," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 117-131.

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