Variogram fitting with a general class of conditionally nonnegative definite functions
Computational Statistics & Data Analysis
Automatic Computation of Zeros of Bessel Functions and Other Special Functions
SIAM Journal on Scientific Computing
Flexible spatio-temporal stationary variogram models
Statistics and Computing
Nonparametric variogram and covariogram estimation with Fourier-Bessel matrices
Computational Statistics & Data Analysis
The effect of the nugget on Gaussian process emulators of computer models
Computational Statistics & Data Analysis
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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 @n. 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.