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With the rapid advancements in technology for data collection, theapplication of the spatial autoregressive (SAR) model has become increasinglyprevalent in real-world analysis, particularly when dealing with largedatasets. However, the commonly used quasi-maximum likelihood estimation (QMLE)for the SAR model is not computationally scalable to handle the data with alarge size. In addition, when establishing the asymptotic properties of theparameter estimators of the SAR model, both weights matrix and regressors areassumed to be nonstochastic in classical spatial econometrics, which is perhapsnot realistic in real applications. Motivated by the machine learningliterature, this paper proposes quasi-score matching estimation for the SARmodel. This new estimation approach is still likelihood-based, butsignificantly reduces the computational complexity of the QMLE. The asymptoticproperties of parameter estimators under the random weights matrix andregressors are established, which provides a new theoretical framework for theasymptotic inference of the SAR-type models. The usefulness of the quasi-scorematching estimation and its asymptotic inference is illustrated via extensivesimulation studies and a case study of an anti-conflict social networkexperiment for middle school students.

Quasi-Score Matching Estimation for Spatial Autoregressive Model with Random Weights Matrix and Regressors