ePrints

Estimation and prediction using generalized wendland covariance functions under fixed domain asymptotics

Lookup NU author(s): Professor Emilio Porcu

Downloads

• Published version [.pdf]

Licence

This is the final published version of an article that has been published in its final definitive form by Institute of Mathematical Statistics, 2019.

For re-use rights please refer to the publisher's terms and conditions.

Abstract

© Institute of Mathematical Statistics, 2019 We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As for the Matérn case, this class allows for a continuous parameterization of smoothness of the underlying Gaussian random field, being additionally compactly supported. The paper is divided into three parts: first, we characterize the equivalence of two Gaussian measures with GW covariance function, and we provide sufficient conditions for the equivalence of two Gaussian measures with Matérn and GW covariance functions. In the second part, we establish strong consistency and asymptotic distribution of the maximum likelihood estimator of the microergodic parameter associated to GW covariance model, under fixed domain asymptotics. The third part elucidates the consequences of our results in terms of (misspecified) best linear unbiased predictor, under fixed domain asymptotics. Our findings are illustrated through a simulation study: the former compares the finite sample behavior of the maximum likelihood estimation of the microergodic parameter with the given asymptotic distribution. The latter compares the finite-sample behavior of the prediction and its associated mean square error when using two equivalent Gaussian measures with Matérn and GW covariance models, using covariance tapering as benchmark.

Publication metadata

Author(s): Bevilacqua M, Furrer R, Faouzi T, Porcu E

Publication type: Article

Publication status: Published

Journal: Annals of Statistics

Year: 2019

Volume: 47

Issue: 2

Pages: 828-856

Print publication date: 01/04/2019

Online publication date: 11/01/2019

Acceptance date: 01/08/2017

Date deposited: 09/04/2019

ISSN (print): 0090-5364

ISSN (electronic): 2168-8966

Publisher: Institute of Mathematical Statistics

URL: https://doi.org/10.1214/17-AOS1652

DOI: 10.1214/17-AOS1652

Altmetrics

Share