Spatial data are widely used in various scenarios of life and are highly valued, and their analysis and research have achieved remarkable results. Spatial data have spatial effects and do not satisfy the assumption of independence; thus, the traditional econometric analysis methods cannot be directly used in spatial models, and the spatial autocorrelation and spatial heterogeneity of spatial data make the research more complicated and difficult. Generalized moment estimation(GMM) is a powerful tool for statistical modeling and inference of spatial data. Considering the case where there is a set of correctly specified moment conditions and another set of possibly misspecified moment conditions for spatial data, this paper proposes a GMM shrinkage method to estimate the unknown parameters for spatial autoregressive model with spatial autoregressive disturbances. The proposed GMM estimators are shown to enjoy oracle properties; i.e., it selects the valid moment conditions consistently from the candidate set and includes them into estimation automatically. The resulting estimator is asymptotically as efficient as the GMM estimator based on all valid moment conditions. Monte Carlo studies show that the method works well in terms of valid moment selection and the finite sample properties of its estimators.

空间数据广泛应用于生活各个场景并受到高度重视，其分析和研究取得了显著成果。空间数据具有空间效应，不满足独立性假设；因此，传统的计量经济分析方法无法直接应用于空间模型，空间数据的空间自相关性和空间异质性使得研究变得更加复杂和困难。广义矩估计（GMM）是空间数据统计建模和推理的强大工具。考虑到空间数据存在一组正确指定的矩条件和另一组可能错误指定的矩条件的情况，提出一种GMM收缩方法来估计具有空间自回归扰动的空间自回归模型的未知参数。所提出的 GMM 估计量被证明具有预言机特性；即，它从候选集中一致地选择有效矩条件，并将它们自动纳入估计中。所得到的估计器与基于所有有效矩条件的 GMM 估计器渐近一样有效。蒙特卡罗研究表明，该方法在有效矩选择及其估计量的有限样本属性方面效果良好。