  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.
