With the rapid advancements in technology for data collection, the application of the spatial autoregressive (SAR) model has become increasingly prevalent in real-world analysis, particularly when dealing with large datasets. However, the commonly used quasi-maximum likelihood estimation (QMLE) for the SAR model is not computationally scalable to handle the data with a large size. In addition, when establishing the asymptotic properties of the parameter estimators of the SAR model, both weights matrix and regressors are assumed to be nonstochastic in classical spatial econometrics, which is perhaps not realistic in real applications. Motivated by the machine learning literature, this paper proposes quasi-score matching estimation for the SAR model. This new estimation approach is still likelihood-based, but significantly reduces the computational complexity of the QMLE. The asymptotic properties of parameter estimators under the random weights matrix and regressors are established, which provides a new theoretical framework for the asymptotic inference of the SAR-type models. The usefulness of the quasi-score matching estimation and its asymptotic inference is illustrated via extensive simulation studies and a case study of an anti-conflict social network experiment for middle school students.

翻译：随着数据收集技术的快速发展，空间自回归模型在实际分析中的应用日益广泛，尤其是在处理大规模数据集时。然而，空间自回归模型常用的准最大似然估计在计算上无法有效扩展以处理大规模数据。此外，在建立空间自回归模型参数估计量的渐近性质时，经典空间计量经济学中假设权重矩阵和解释变量均为非随机的，这在实际应用中可能并不现实。受机器学习文献的启发，本文提出了空间自回归模型的准得分匹配估计方法。这一新的估计方法仍基于似然函数，但显著降低了准最大似然估计的计算复杂度。我们建立了随机权重矩阵和解释变量下参数估计量的渐近性质，为空间自回归型模型的渐近推断提供了新的理论框架。通过大量模拟研究及一项针对中学生的反冲突社交网络实验案例研究，验证了准得分匹配估计及其渐近推断的有效性。