🤖 AI Summary
This paper addresses two key limitations of quasi-maximum likelihood estimation (QMLE) for large-scale spatial autoregressive (SAR) models: its computational intractability and the unrealistic reliance of classical asymptotic theory on non-stochastic weight matrices and regressors. To overcome these, we propose quasi-score matching estimation (QSM). QSM establishes, for the first time, a rigorous asymptotic framework for SAR models under stochastic weight matrices and stochastic regressors, proving consistency and asymptotic normality of the estimator. Computationally, QSM avoids high-dimensional matrix inversion and iterative optimization—substantially reducing complexity relative to QMLE. Monte Carlo simulations and an empirical application to a middle-school anti-conflict social network demonstrate that QSM achieves high computational efficiency, accurate statistical inference, and robustness to model misspecification. Thus, QSM provides a scalable and theoretically sound alternative for large-scale spatial econometric analysis.
📝 Abstract
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 developed based on the likelihood, 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.
