The spatial autoregressive (SAR) model has been widely applied in various
empirical economic studies to characterize the spatial dependence among
subjects. However, the precision of estimating the SAR model diminishes when
the sample size of the target data is limited. In this paper, we propose a new
transfer learning framework for the SAR model to borrow the information from
similar source data to improve both estimation and prediction. When the
informative source data sets are known, we introduce a two-stage algorithm,
including a transferring stage and a debiasing stage, to estimate the unknown
parameters and also establish the theoretical convergence rates for the
resulting estimators. If we do not know which sources to transfer, a
transferable source detection algorithm is proposed to detect informative
sources data based on spatial residual bootstrap to retain the necessary
spatial dependence. Its detection consistency is also derived. Simulation
studies demonstrate that using informative source data, our transfer learning
algorithm significantly enhances the performance of the classical two-stage
least squares estimator. In the empirical application, we apply our method to
the election prediction in swing states in the 2020 U.S. presidential election,
utilizing polling data from the 2016 U.S. presidential election along with
other demographic and geographical data. The empirical results show that our
method outperforms traditional estimation methods.

本文提出了一种新的转移学习框架，借助相似的源数据改善空间自相关模型的估计和预测精度，包括一个转移阶段和一个去偏阶段的两阶段算法用于估计未知参数，并建立了相应估计器的理论收敛速度；如果不知道哪些源数据需要转移，提出了一种基于空间残差自助法的可转移源数据检测算法以保留必要的空间依赖性，并得出了其检测一致性。通过仿真实验表明，使用具有信息的源数据，该转移学习算法显著提高了经典的两阶段最小二乘估计器的性能。在实证应用中，我们将该方法应用于 2020 年美国总统选举中摇摆州的选举预测，利用 2016 年美国总统选举的民意调查数据以及其他人口和地理数据。实证结果表明我们的方法优于传统估计方法。