edu.ucar.opensky::articles:18099 UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact 2025-12-26T15:11:56.856238 ISO 19115-2 Geographic Information - Metadata - Part 2: Extensions for Imagery and Gridded Data ISO 19115-2:2009(E) https://n2t.org/ark:/85065/d7pv6mxs Covariance tapering for likelihood-based estimation in large spatial data sets 2008-12-01T00:00:00Z publication https://n2t.org/ark:/85065/d7pv6mxs https://doi.org/10.1198/016214508000000959 Kaufman, C. author Schervish, M. author Nychka, Douglas author UCAR/NCAR - Library publisher Maximum likelihood is an attractive method of estimating covariance parameters in spatial models based on Gaussian processes. But calculating the likelihood can be computationally infeasible for large data sets, requiring O(n³) calculations for a data set with n observations. This article proposes the method of covariance tapering to approximate the likelihood in this setting. In this approach, covariance matrixes are "tapered," or multiplied element wise by a sparse correlation matrix. The resulting matrixes can then be manipulated using efficient sparse matrix algorithms. We propose two approximations to the Gaussian likelihood using tapering. One of these approximations simply replaces the model covariance with a tapered version, whereas the other is motivated by the theory of unbiased estimating equations. Focusing on the particular case of the Matérn class of covariance functions, we give conditions under which estimators maximizing the tapering approximations are, like the maximum likelihood estimator, strongly consistent. Moreover, we show in a simulation study that the tapering estimators can have sampling densities quite similar to that of the maximum likelihood estimator, even when the degree of tapering is severe. We illustrate the accuracy and computational gains of the tapering methods in an analysis of yearly total precipitation anomalies at weather stations in the United States. UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact PDF Text theme Resource Type 2016-01-01T00:00:00Z publication Copyright 2008 Authors. An edited version of this article was published by the American Statistical Association. None eng geoscientificInformation