Space-Time Estimation and Prediction under Infill Asymptotics with Compactly Supported Covariance Functions

Tarik Faouzi, Emilio Porcu, Moreno Bevilacqua
2022 Statistica sinica  
We study estimation and prediction of Gaussian processes with space-time covariance models belonging to the Dynamical Generalized Wendland family (DGW) (Porcu et al., 2020, Statistica Sinica), 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 (Ip and Li, 2017, Statistica Sinica). The results of the paper are classified into two parts. In the first part, we
more » ... ish strong consistency and asymptotic normality for the maximum likelihood estimator of the microergodic parameter associated to the DGW covariance model, under fixed-domain asymptotics. The last part focuses on optimal kriging prediction under the DGW model and asymptotically correct estimation of mean square error using a misspecified model. Theoretical results are in turn based on equivalence of Gaussian measures under some given families of space-time covariance functions, where both space or time are compact. Such technical results are provided in the Online Supplement to this paper.
doi:10.5705/ss.202020.0010 fatcat:7gzlsznuife6dd5rnaqmmdmdle