Abstract
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.
Citation
Wei-Liem Loh. "Estimating the smoothness of a Gaussian random field from irregularly spaced data via higher-order quadratic variations." Ann. Statist. 43 (6) 2766 - 2794, December 2015. https://doi.org/10.1214/15-AOS1365
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