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Asymptotic properties of multivariate tapering for estimation and prediction


Furrer, Reinhard; Bachoc, François; Du, Juan (2016). Asymptotic properties of multivariate tapering for estimation and prediction. Journal of Multivariate Analysis, 149:177-191.

Abstract

Parameter estimation for and prediction of spatially or spatio-temporally correlated random processes are used in many areas and often require the solution of a large linear system based on the covariance matrix of the observations. In recent years, the dataset sizes to which these methods are applied have steadily increased such that straightforward statistical tools are computationally too expensive to be used. In the univariate context, tapering, i.e., creating sparse approximate linear systems, has been shown to be an efficient tool in both the estimation and prediction settings. The asymptotic properties are derived under an infill asymptotic setting. In this paper we use a domain increasing framework for estimation and prediction using multivariate tapering. Under this asymptotic regime we prove that tapering (one-tapered form) preserves the consistency of the untapered maximum likelihood estimator and show that tapering has asymptotically the same mean squared prediction error as using the corresponding untapered predictor. The theoretical results are illustrated with simulations.

Abstract

Parameter estimation for and prediction of spatially or spatio-temporally correlated random processes are used in many areas and often require the solution of a large linear system based on the covariance matrix of the observations. In recent years, the dataset sizes to which these methods are applied have steadily increased such that straightforward statistical tools are computationally too expensive to be used. In the univariate context, tapering, i.e., creating sparse approximate linear systems, has been shown to be an efficient tool in both the estimation and prediction settings. The asymptotic properties are derived under an infill asymptotic setting. In this paper we use a domain increasing framework for estimation and prediction using multivariate tapering. Under this asymptotic regime we prove that tapering (one-tapered form) preserves the consistency of the untapered maximum likelihood estimator and show that tapering has asymptotically the same mean squared prediction error as using the corresponding untapered predictor. The theoretical results are illustrated with simulations.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:April 2016
Deposited On:02 Feb 2017 07:16
Last Modified:19 Aug 2018 03:39
Publisher:Elsevier
ISSN:0047-259X
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.jmva.2016.04.006
Project Information:
  • : FunderSNSF
  • : Grant ID200021_143282
  • : Project TitleMultivariate modeling of large non-stationary spatial and spatio-temporal climate fields

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