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On a class of non-stationary, compactly supported spatial covariance functions

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Abstract

Globally supported covariance functions are generally associated with dense covariance matrices, meaning severe numerical problems in solution feasibility. These problems can be alleviated by considering methods yielding sparse covariance matrices. Indeed, having many zero entries in the covariance matrix can both greatly reduce computer storage requirements and the number of floating point operations needed in computation. Compactly supported covariance functions considerably reduce the computational burden of kriging, and allow the use of computationally efficient sparse matrix techniques, thus becoming a core aspect in spatial prediction when dealing with massive data sets. However, most of the work done in the context of compactly supported covariance functions has been carried out in the stationary context. This assumption is not generally met in practical and real problems, and there has been a growing recognition of the need for non-stationary spatial covariance functions in a variety of disciplines. In this paper we present a new class of non-stationary, compactly supported spatial covariance functions, which adapts a class of convolution-based flexible models to non-stationary situations. Some particular examples, computational issues, and connections with existing models are considered.

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Acknowledgements

The authors are indebted to two referees and an AE for useful discussions and comments that improved an earlier version of the manuscript. We also would like to thank F. Rodríguez-Cortés for his help with programming. The work was partially funded by grant MTM2010-14961 from the Spanish Ministry of Science and Education.

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Authors and Affiliations

  1. Department of Mathematics, University Jaume I, Campus Riu Sec, 12071, Castellon, Spain

    J. Mateu

  2. Department of Statistics, University of Castilla-La-Mancha, 45071, Toledo, Spain

    G. Fernández-Avilés & J. M. Montero

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  1. J. Mateu
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  2. G. Fernández-Avilés
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  3. J. M. Montero
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Correspondence to J. Mateu.

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Mateu, J., Fernández-Avilés, G. & Montero, J.M. On a class of non-stationary, compactly supported spatial covariance functions. Stoch Environ Res Risk Assess 27, 297–309 (2013). https://doi.org/10.1007/s00477-011-0510-8

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