Estimating the smoothness of a Gaussian random field from irregularly spaced data via higher-order quadratic variations
The Annals of Statistics · 2015 · Volume 43 · Issue 6
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.
Keywords
62M30, 62M40, Gaussian random field, higher-order quadratic variation, irregularly spaced data, Matérn covariance, smoothness estimation
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