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.

翻译：本文研究了当数据为空间域（$\mathbb{Z}^d$ 中网格点，$d\geqslant 2$）上的观测时，多元线性回归模型中的变量选择问题。我们采用一种准则，通过两个参数来刻画相关变量子集，并基于空间依赖观测提出了这些参数的估计方法。在特定假设下，我们证明了所提方法的一致性。为评估所提方法在有限样本下的表现，本文给出了一项与现有方法进行比较的模拟研究。