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 journalArticle

4 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1737-1747
Number of pages11
JournalComputational Statistics and Data Analysis
Volume56
Issue number6
DOIs
StatePublished - Jun 2012

Fingerprint

Semivariogram
Parametric Model
Bochner's Theorem
Bessel function of the first kind
Semiparametric Methods
Estimator
Spatial Modeling
Bessel functions
Vertex of a graph
Statistical Inference
Efficacy
Roots
Restriction
Demonstrate
Simulation
Class
Form

Keywords

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

ASJC Scopus subject areas

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

Cite this

A new class of semiparametric semivariogram and nugget estimators. / Carmack, Patrick S.; Spence, Jeffrey S.; Schucany, William R.; Gunst, Richard F.; Lin, Qihua; Haley, Robert W.

In: Computational Statistics and Data Analysis, Vol. 56, No. 6, 06.2012, p. 1737-1747.

Research output: Contribution to journalArticle

Carmack, Patrick S. ; Spence, Jeffrey S. ; Schucany, William R. ; Gunst, Richard F. ; Lin, Qihua ; Haley, Robert W. / A new class of semiparametric semivariogram and nugget estimators. In: Computational Statistics and Data Analysis. 2012 ; Vol. 56, No. 6. pp. 1737-1747.
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