This work focuses on variable selection for spatial regression models, with locations on irregular lattices and errors according to Conditional or Simultaneous Auto-Regressive (CAR or SAR) models. The strategy is to whiten the residuals by estimating their spatial covariance matrix and then proceed by performing the standard L1-penalized regression LASSO for independent data on the transformed model. A result is stated that proves the sign consistency for general dependent errors provided that the transformed design matrix fulfills standard assumptions for the LASSO procedure and that the estimate of the residual covariance matrix is consistent. Then sufficient conditions on the weight matrix of the SAR or CAR model are given that ensure those conditions hold. A simulation study is driven that shows this method gives good result in terms of variables selection, while some underestimation of the coefficients is noted. It is compared to a strategy that estimates both the regression and the covariance parameters in a LARS procedure. Coefficient are better estimated with the Least Angle Regression (LARS) procedure but it gives in some cases much more false positive in the variable selection. The application is on the regression of income data in rural area of Uruguay on a set of covariates describing socio-economic characteristics of the households.

这项工作的重点是空间回归模型的变量选择，根据条件或同时自回归（CAR 或 SAR）模型，在不规则格上的位置和错误。该策略是通过估计它们的空间协方差矩阵来白化残差，然后通过对变换模型上的独立数据执行标准 L1 惩罚回归 LASSO 继续进行。如果转换后的设计矩阵满足 LASSO 程序的标准假设并且残差协方差矩阵的估计值是一致的，则说明结果证明了一般相关误差的符号一致性。然后给出 SAR 或 CAR 模型的权重矩阵的充分条件，以确保这些条件成立。一项模拟研究表明，该方法在变量选择方面给出了良好的结果，同时注意到了一些对系数的低估。它与在 LARS 过程中估计回归和协方差参数的策略进行比较。使用最小角回归 (LARS) 程序可以更好地估计系数，但它在某些情况下会在变量选择中产生更多的误报。该应用程序是关于乌拉圭农村地区收入数据对一组描述家庭社会经济特征的协变量的回归。使用最小角回归 (LARS) 程序可以更好地估计系数，但它在某些情况下会在变量选择中产生更多的误报。该应用程序是关于乌拉圭农村地区收入数据对一组描述家庭社会经济特征的协变量的回归。使用最小角回归 (LARS) 程序可以更好地估计系数，但它在某些情况下会在变量选择中产生更多的误报。该应用程序是关于乌拉圭农村地区收入数据对一组描述家庭社会经济特征的协变量的回归。