ESTIMATION AND PREDICTION USING GENERALIZED WENDLAND COVARIANCE FUNCTIONS UNDER FIXED DOMAIN ASYMPTOTICS

• 成果类型: Article
• 署名作者: Bevilacqua, Moreno; Faouzi, Tarik; Furrer, Reinhard; Porcu, Emilio
• 署名单位: Universidad de Valparaiso; Universidad del Bio-Bio; University of Zurich; University of Zurich; Newcastle University - UK; Universidad de Atacama
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1652
• 发表日期: 2019
• 页码: 828-856
• 关键词: random-field; linear predictions; optimality

摘要

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 Matern 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 Matern 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 Matern and GW covariance models, using covariance tapering as benchmark.