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

M. Bevilacqua, R. Furrer, T. Faouzi, E. Porcu

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

37 Citas (Scopus)

Resumen

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.

Idioma originalInglés
Páginas (desde-hasta)828-856
Número de páginas29
PublicaciónAnnals of Statistics
Volumen47
N.º2
DOI
EstadoPublicada - abr. 2019

Huella

Profundice en los temas de investigación de 'Estimation and prediction using generalized wendland covariance functions under fixed domain asymptotics'. En conjunto forman una huella única.

Citar esto