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2021 Smoothness estimation of nonstationary Gaussian random fields from irregularly spaced data observed along a curve
Jun Wen, Saifei Sun, Wei-Liem Loh
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Electron. J. Statist. 15(2): 6071-6150 (2021). DOI: 10.1214/21-EJS1941

Abstract

This article considers estimating the smoothness parameter of a class of nonstationary Gaussian random fields on Rd using irregularly spaced data observed along a curve. The set of covariance functions includes a nonstationary version of the Matérn covariance function as well as isotropic Matérn covariance function. Smoothness estimators are constructed via higher-order quadratic variations. Under mild conditions, these estimators are shown to be strongly consistent and convergence rate upper bounds are established with respect to fixed-domain asymptotics. Simulations indicate that the proposed estimators perform well for moderate sample sizes.

Funding Statement

The authors were supported in part by AcRF Tier 1 Grant R-155-000-209-114.

Acknowledgments

We would like to thank Professor Domenico Marinucci, an Associate Editor and two referees for their comments and suggestions that led to numerous improvements to this article.

Citation

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Jun Wen. Saifei Sun. Wei-Liem Loh. "Smoothness estimation of nonstationary Gaussian random fields from irregularly spaced data observed along a curve." Electron. J. Statist. 15 (2) 6071 - 6150, 2021. https://doi.org/10.1214/21-EJS1941

Information

Received: 1 August 2021; Published: 2021
First available in Project Euclid: 27 December 2021

Digital Object Identifier: 10.1214/21-EJS1941

Subjects:
Primary: 62M30
Secondary: 62F12

Keywords: convergence rate , curved line transect sampling , fixed-domain asymptotics , irregularly spaced data , nonstationary Gaussian random field , Quadratic Variation , smoothness estimation

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Vol.15 • No. 2 • 2021
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