Data-driven neighborhood selection of a Gaussian field

The nonparametric covariance estimation of a stationary Gaussian field XX 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 m̂ by a penalization method and estimating the covariance of XX in the space of Gaussian Markov random fields (GMRFs) with neighborhood m̂. 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.