A new class of semiparametric semivariogram and nugget estimators

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

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1737-1747
Number of pages11
JournalComputational Statistics and Data Analysis
Issue number6
StatePublished - Jun 2012


  • Bessel basis
  • Isotropic
  • Negative definiteness
  • Node space
  • Nonparametric
  • Regular lattice
  • Unsupervised brain imaging

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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