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A new class of semiparametric semivariogram and nugget estimators

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  • Carmack, Patrick S.
  • Spence, Jeffrey S.
  • Schucany, William R.
  • Gunst, Richard F.
  • Lin, Qihua
  • Haley, Robert W.

Abstract

Several authors have proposed nonparametric semivariogram estimators. Shapiro and Botha (1991) did so by application of Bochner’s theorem and Cherry et al. (1996) further investigated this technique where it performed favorably against parametric estimators even when data were generated under the parametric model. While the former makes allowances for a prescribed nugget and the latter outlines a possible approach, neither of these demonstrate nugget estimation in practice, which is essential to spatial modeling and proper statistical inference. We propose a modified form of this method, which admits practical nugget estimation and broadens the basis. This is achieved by a simple change to the basis and an appropriate restriction of the node space as dictated by the first root of the Bessel function of the first kind of order ν. The efficacy of this new unsupervised semiparametric method is demonstrated via application and simulation, where it is shown to be comparable with correctly specified parametric models while outperforming misspecified ones. We conclude with remarks about selecting the appropriate basis and node space definition.

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  • Carmack, Patrick S. & Spence, Jeffrey S. & Schucany, William R. & Gunst, Richard F. & Lin, Qihua & Haley, Robert W., 2012. "A new class of semiparametric semivariogram and nugget estimators," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1737-1747.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1737-1747
    DOI: 10.1016/j.csda.2011.10.017
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    References listed on IDEAS

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    1. Shapiro, A. & Botha, J. D., 1991. "Variogram fitting with a general class of conditionally nonnegative definite functions," Computational Statistics & Data Analysis, Elsevier, vol. 11(1), pages 87-96, January.
    2. Spence, Jeffrey S. & Carmack, Patrick S. & Gunst, Richard F. & Schucany, William R. & Woodward, Wayne A. & Haley, Robert W., 2007. "Accounting for Spatial Dependence in the Analysis of SPECT Brain Imaging Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 464-473, June.
    3. Genton, Marc G. & Gorsich, David J., 2002. "Nonparametric variogram and covariogram estimation with Fourier-Bessel matrices," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 47-57, November.
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    Cited by:

    1. Andrianakis, Ioannis & Challenor, Peter G., 2012. "The effect of the nugget on Gaussian process emulators of computer models," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4215-4228.
    2. Sompop Moonchai & Nawinda Chutsagulprom, 2020. "Semiparametric Semivariogram Modeling with a Scaling Criterion for Node Spacing: A Case Study of Solar Radiation Distribution in Thailand," Mathematics, MDPI, vol. 8(12), pages 1-16, December.

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