IDEAS home Printed from
   My bibliography  Save this article

Data-driven neighborhood selection of a Gaussian field


  • Verzelen, Nicolas


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

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. 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.
    2. 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, vol. 102, pages 726-735, June.
    3. 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.
    4. Cressie, Noel & Verzelen, Nicolas, 2008. "Conditional-mean least-squares fitting of Gaussian Markov random fields to Gaussian fields," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2794-2807, January.
    5. HÃ¥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.
    6. 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, vol. 98, pages 77-89, January.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:54:y:2010:i:5:p:1355-1371. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.