Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes

JOURNAL OF MULTIVARIATE ANALYSIS

卷:125

Article

Bachoc, Francois^1,2 

[1] CEA Saclay, LGLS, STMF, DM2S,DEN, F-91191 Gif Sur Yvette, France

[2] Univ Paris Diderot, Lab Probabilites & Modeles Aleatoires, F-75205 Paris 13, France

关键词: Uncertainty quantification;    Metamodel;    Kriging;    Covariance parameter estimation;    Maximum likelihood;    Leave-one-out;    Increasing-domain asymptotics;   

DOI  :  10.1016/j.jmva.2013.11.015

来源: Elsevier

【 摘 要 】

Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar regularity parameter. Consistency and asymptotic normality are proved for the Maximum Likelihood and Cross Validation estimators of the covariance parameters. The asymptotic covariance matrices of the covariance parameter estimators are deterministic functions of the regularity parameter. By means of an exhaustive study of the asymptotic covariance matrices, it is shown that the estimation is improved when the regular grid is strongly perturbed. Hence, an asymptotic confirmation is given to the commonly admitted fact that using groups of observation points with small spacing is beneficial to covariance function estimation. Finally, the prediction error, using a consistent estimator of the covariance parameters, is analyzed in detail. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free