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Data-driven neighborhood selection of a Gaussian field

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  • Verzelen, Nicolas

Abstract

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 by a penalization method and estimating the covariance of X in the space of Gaussian Markov random fields (GMRFs) with neighborhood . 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.

Suggested Citation

  • Verzelen, Nicolas, 2010. "Data-driven neighborhood selection of a Gaussian field," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1355-1371, May.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:5:p:1355-1371
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    References listed on IDEAS

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