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We study estimation and prediction of Gaussian random fields with covariancemodels belonging to the generalized Wendland (GW) class, under fixed domainasymptotics. As the Mat\'ern case, this class allows a continuousparameterization of smoothness of the underlying Gaussian random field, beingadditionally compactly supported. The paper is divided into two parts: First,we characterize the equivalence of two Gaussian measures with GW covariancefunction, and we provide sufficient conditions for the equivalence of twoGaussian measures with Mat\'ern and GW covariance functions. We elucidate theconsequences of these facts in terms of (misspecified) best linear unbiasedpredictors. In the second part, we establish strong consistency and asymptoticdistribution of the maximum likelihood estimator of the microergodic parameterassociated to GW covariance model, under fixed domain asymptotics. Our findingsare illustrated through a simulation study: The first compares the finitesample behavior of the maximum likelihood estimation of the microergodicparameter with the given asymptotic distribution. We then compare thefinite-sample behavior of the prediction and its associated mean square errorwhen using two equivalent Gaussian measures with Mat\'ern and GW covariancemodel, using covariance tapering as benchmark.

Estimation and Prediction using generalized Wendland Covariance Functions under fixed domain asymptotics