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Data-driven neighborhood selection of a Gaussian field. (English) Zbl 1464.62174

Summary: The nonparametric covariance estimation of a stationary Gaussian field \(X\) observed on a lattice is investigated. To tackle this issue, a neighborhood selection procedure has been recently introduced. This procedure amounts to selecting a neighborhood \(\widehat m\) by a penalization method and estimating the covariance of \(X\) in the space of Gaussian Markov random fields (GMRFs) with neighborhood \(\widehat m\). Such a strategy is shown to satisfy oracle inequalities as well as minimax adaptive properties. However, it suffers several drawbacks which make the method difficult to apply in practice: the penalty depends on some unknown quantities and the procedure is only defined for toroidal lattices. The contribution is threefold. Firstly, a data-driven algorithm is proposed for tuning the penalty function. Secondly, the procedure is extended to non-toroidal lattices. Thirdly, numerical study illustrates the performances of the method on simulated examples. These simulations suggest that Gaussian Markov random field selection is often a good alternative to variogram estimation.

MSC:

62-08 Computational methods for problems pertaining to statistics
62M40 Random fields; image analysis
60G60 Random fields

Software:

geoR; RandomFields; R; GMRFLib
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Full Text: DOI arXiv

References:

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