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Data-driven neighborhood selection of a Gaussian field

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  • Verzelen, Nicolas
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 54 (2010)
    Issue (Month): 5 (May)
    Pages: 1355-1371

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    Handle: RePEc:eee:csdana:v:54:y:2010:i:5:p:1355-1371

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    Web page: http://www.elsevier.com/locate/csda

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    1. Dass S.C. & Nair V.N., 2003. "Edge Detection, Spatial Smoothing, and Image Reconstruction With Partially Observed Multivariate Data," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 98, pages 77-89, January.
    2. Song, Hae-Ryoung & Fuentes, Montserrat & Ghosh, Sujit, 2008. "A comparative study of Gaussian geostatistical models and Gaussian Markov random field models," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1681-1697, September.
    3. Cressie, Noel & Verzelen, Nicolas, 2008. "Conditional-mean least-squares fitting of Gaussian Markov random fields to Gaussian fields," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 52(5), pages 2794-2807, January.
    4. H�vard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392.
    5. Guyon, Xavier & Yao, Jian-feng, 1999. "On the Underfitting and Overfitting Sets of Models Chosen by Order Selection Criteria," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 221-249, August.
    6. IM, Hae Kyung & Stein, Michael L. & Zhu, Zhengyuan, 2007. "Semiparametric Estimation of Spectral Density With Irregular Observations," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 102, pages 726-735, June.
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