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Nonparametric estimation of the variogram and its spectrum

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  • Chunfeng Huang
  • Tailen Hsing
  • Noel Cressie

Abstract

In the study of intrinsically stationary spatial processes, a new nonparametric variogram estimator is proposed through its spectral representation. The methodology is based on estimation of the variogram's spectrum by solving a regularized inverse problem through quadratic programming. The estimated variogram is guaranteed to be conditionally negative-definite. Simulation shows that our estimator is flexible and generally has smaller mean integrated squared error than the parametric estimator under model misspecification. Our methodology is applied to a spatial dataset of decadal temperature changes. Copyright 2011, Oxford University Press.

Suggested Citation

  • Chunfeng Huang & Tailen Hsing & Noel Cressie, 2011. "Nonparametric estimation of the variogram and its spectrum," Biometrika, Biometrika Trust, vol. 98(4), pages 775-789.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:4:p:775-789
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    File URL: http://hdl.handle.net/10.1093/biomet/asr056
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    Cited by:

    1. Tata Subba Rao & Granville Tunnicliffe Wilson & Tata Subba Rao & Gyorgy Terdik, 2017. "On the Frequency Variogram and on Frequency Domain Methods for the Analysis of Spatio-Temporal Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 308-325, March.
    2. Zhang, Haimeng & Huang, Chunfeng, 2014. "A note on processes with random stationary increments," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 153-161.
    3. Vidoli, Francesco & Canello, Jacopo, 2016. "Controlling for spatial heterogeneity in nonparametric efficiency models: An empirical proposal," European Journal of Operational Research, Elsevier, vol. 249(2), pages 771-783.

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