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

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

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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

Information

Received: 1 March 2015; Revised: 1 July 2015; Published: December 2015
First available in Project Euclid: 7 October 2015

zbMATH: 1327.62482
MathSciNet: MR3405611
Digital Object Identifier: 10.1214/15-AOS1365

Subjects:
Primary: 62M30
Secondary: 62M40

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 6 • December 2015
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