ll giorno lunedì13 febbraio alle ore 11.00 presso la aula seminari del Dismeq al IV piano dell'edificio U7, il prof. Emilio Porcu del Department of Mathematics della University Federico Santa Maria di Valparaiso terrà un seminario su
Estimation and Prediction using Wendland covariance functions under Infill Asymptotics
Abstract
We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As the Matlern case, this class allows a continuous parameterization of smoothness of the underlying Gaussian random field, being additionally compactly supported. The paper is divided into two 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 Matlern and GW covariance functions. We elucidate the consequences of these facts in terms of (misspecified) best linear unbiased predictors. 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. 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 Matlern and GW covariance model, using covariance tapering as benchmark.
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