Data-driven neighborhood selection of a Gaussian field

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

• Publication year

  2009

• Venue

  Computational Statistics & Data Analysis

• Publication date

  2009-01-15

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1016/j.csda.2009.12.001arXiv 0901.2213
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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