Abstract Spatial dependent data frequently occur in spatial econometrics and endemiology. In this work, we propose a class of penalized robust regression estimators based on exponential squared loss with independent and identical distributed errors for general spatial autoregressive models. A penalized exponential squared loss with the adaptive lasso penalty is employed for simultaneous model selection and parameter estimation. Under mild conditions, we establish the asymptotic and oracle property of the proposed estimators The induced nonconvex nondifferentiable mathematical programming offer challenges for solving algorithms. We specially design a block coordinate descent (BCD) algorithm equipped with CCCP procedure for efficiently solving the subproblem. Moreover, we provide a convergence guarantee of the BCD algorithm. Every limit point of the iterated solutions is proved a stationary point. We also present a convergence speed of spatial weight ρ k . Numerical studies illustrate that the proposed method is particularly robust and applicable when the outliers or intensive noise exist in the observations or the estimated spatial weight matrix is inaccurate. All the source code could be freely downloaded from https://github.com/Isaac-QiXing/SAR .

中文翻译：

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空间自回归模型的具有指数平方损失的稳健变量选择

摘要 空间相关数据经常出现在空间计量经济学和地方病学中。在这项工作中，我们为一般空间自回归模型提出了一类基于指数平方损失的惩罚鲁棒回归估计器，具有独立和相同的分布误差。具有自适应套索惩罚的惩罚指数平方损失用于同时进行模型选择和参数估计。在温和的条件下，我们建立了所提出的估计量的渐近和预言性质。诱导的非凸不可微的数学规划为求解算法提供了挑战。我们专门设计了一种配备 CCCP 程序的块坐标下降 (BCD) 算法，以有效解决子问题。此外，我们提供了 BCD 算法的收敛保证。证明迭代解的每个极限点都是一个驻点。我们还提出了空间权重 ρ k 的收敛速度。数值研究表明，当观测中存在异常值或强噪声或估计的空间权重矩阵不准确时，所提出的方法特别稳健和适用。所有源代码均可从 https://github.com/Isaac-QiXing/SAR 免费下载。