SPACE-TIME ESTIMATION AND PREDICTION UNDER FIXED-DOMAIN ASYMPTOTICS WITH COMPACTLY SUPPORTED COVARIANCE FUNCTIONS

Tarik Faouzi, Emilio Porcu, Moreno Bevilacqua

Research output: Contribution to journalArticlepeer-review

Abstract

We study the estimation and prediction of Gaussian processes with space-time covariance models belonging to the dynamical generalized Wendland (DGW) family, under fixed-domain asymptotics. Such a class is nonseparable, has dynamical compact supports, and parameterizes differentiability at the origin similarly to the space-time Matérn class. Our results are presented in two parts. First, we establish the strong consistency and asymptotic normality for the maximum likelihood estimator of the microergodic parameter associated with the DGW covariance model, under fixed-domain asymptotics. The second part focuses on optimal kriging prediction under the DGW model and an asymptotically correct estimation of the mean squared error using a misspecified model. Our theoretical results are, in turn, based on the equivalence of Gaussian measures under some given families of space-time covariance functions, where both space or time are compact. The technical results are provided in the online Supplementary material.

Original languageEnglish
Pages (from-to)1187-1203
Number of pages17
JournalStatistica Sinica
Volume32
Issue number3
DOIs
StatePublished - Jul 2022
Externally publishedYes

Keywords

  • Fixed-domain asymptotics
  • maximum likelihood
  • microergodic parameter
  • space-time generalized wendland family

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