  This paper deals with variable selection in multivariate linear regression
model when the data are observations on a spatial domain being a grid of sites
in $\mathbb{Z}^d$ with $d\geqslant 2$. We use a criterion that allows to
characterize the subset of relevant variables as depending on two parameters,
and we propose estimators for these parameters based on spatially dependent
observations. We prove the consistency, under specified assumptions, of the
method thus proposed. A simulation study made in order to assess the
finite-sample behaviour of the proposed method with comparison to existing ones
is presented.
