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Estimating the smoothness of a Gaussian random field from irregularly spaced data via higher-order quadratic variations
Wei-Liem Loh · 2015-10-29 · via math.ST updates on arXiv.org

This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of the corresponding fixed-domain asymptotic theory. In particular, we consider: (i) higher-order quadratic variations using nonequispaced line transect data, (ii) second-order quadratic variations from a sample of Gaussian random field observations taken along a smooth curve in ${\mathbb{R}}^2$, (iii) second-order quadratic variations based on deformed lattice data on ${\mathbb{R}}^2$. Smoothness estimators are proposed that are strongly consistent under mild assumptions. Simulations indicate that these estimators perform well for moderate sample sizes.

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