A new class of semiparametric semivariogram and nugget estimators

Several authors have proposed nonparametric semivariogram estimators. Shapiro & Botha (1991) did so by application of Bochner’s theorem and Cherry, Banfield & Quimby (1996) further investigated this technique where it performed favorably against parametric estimators even when data were generated under the parametric model. While this approach is sound, it lacks nugget estimation which is essential to spatial modeling and proper statistical inference. We propose a modified form of this method, which admits 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 method is demonstrated via simulation. We conclude with remarks about selecting the appropriate basis and node space definition.