Spatial autoregressive models typically rely on the assumption that the spatial dependence structure is known in advance and is represented by a deterministic spatial weights matrix, although it is unknown in most empirical applications. Thus, we investigate the estimation of sparse spatial dependence structures for regular lattice data. In particular, an adaptive least absolute shrinkage and selection operator (lasso) is used to select and estimate the individual nonzero connections of the spatial weights matrix. To recover the spatial dependence structure, we propose cross-sectional resampling, assuming that the random process is exchangeable. The estimation procedure is based on a two-step approach to circumvent simultaneity issues that typically arise from endogenous spatial autoregressive dependencies. The two-step adaptive lasso approach with cross-sectional resampling is verified using Monte Carlo simulations. Eventually, we apply the procedure to model nitrogen dioxide $({\text{NO}}_2)$ concentrations and show that estimating the spatial dependence structure contrary to using prespecified weights matrices improves the prediction accuracy considerably.

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规则格数据的空间加权矩阵估计——具有横截面重采样的自适应套索方法

空间自回归模型通常依赖于空间依赖结构是预先已知的假设并且由确定性空间权重矩阵表示，尽管它在大多数经验应用中是未知的。因此，我们研究了规则格数据的稀疏空间依赖结构的估计。特别是，自适应最小绝对收缩和选择算子 (lasso) 用于选择和估计空间权重矩阵的各个非零连接。为了恢复空间依赖结构，我们提出了横截面重采样，假设随机过程是可交换的。估计过程基于两步方法来规避通常由内生空间自回归依赖性引起的同时性问题。使用蒙特卡罗模拟验证了具有横截面重采样的两步自适应套索方法。最终，我们应用该程序来模拟二氧化氮$({\text{不}}_2)$浓度并表明，与使用预先指定的权重矩阵相反，估计空间依赖结构可以显着提高预测精度。