Covariance Tapering for Interpolation of Large Spatial Datasets
نویسندگان
چکیده
منابع مشابه
Covariance Tapering for Interpolation of Large Spatial Datasets
Interpolation of a spatially correlated random process is used in many areas. The best unbiased linear predictor, often called kriging predictor in geostatistical science, requires the solution of a large linear system based on the covariance matrix of the observations. In this article, we show that tapering the correct covariance matrix with an appropriate compactly supported covariance functi...
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Maximum likelihood is an attractive method of estimating covariance parameters in spatial models based on Gaussian processes. However, calculating the likelihood can be computationally infeasible for large datasets, requiring O(n3) calculations for a dataset with n observations. This article proposes the method of covariance tapering to approximate the likelihood in this setting. In this approa...
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In the analysis of spatial data, the inverse of the covariance matrix needs to be calculated. For example, the inverse is needed for best linear unbiased prediction or kriging, and is repeatedly calculated in the maximum likelihood estimation or the Bayesian inferences. Since the spatial sample size can be quite large, operations on the large covariance matrix can be a numerical challenge if no...
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Bandable covariance matrices are often used to model the dependence structure of variables that follow a nature order. It has been shown that the tapering covariance estimator attains the optimal minimax rates of convergence for estimating large bandable covariance matrices. The estimation risk critically depends on the choice of the tapering parameter.We develop a Stein’s Unbiased Risk Estimat...
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Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statistics face tremendous challenges due to the prohibitive computational burden. Various approximation methods have been introduced to reduce the computational cost. However, most of them rely on unrealistic assumptions of th...
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ژورنال
عنوان ژورنال: Journal of Computational and Graphical Statistics
سال: 2006
ISSN: 1061-8600,1537-2715
DOI: 10.1198/106186006x132178