Abstract：Spatial autoregressive (SAR) models and extensions are important tools for studying network effects. However, with an increasing emphasis on data privacy, data providers often implement privacy protection measures that make SAR models inapplicable. In this study, we introduce a privacy-protected SAR model with noise-added response and covariates to meet privacy-protection requirements. However, in this scenario, the traditional quasi-maximum likelihood estimator becomes infeasible because the likelihood function cannot be directly formulated. To address this issue, we first consider an explicit expression for the likelihood function with only noise-added responses. Then, we develop techniques to correct the biases for derivatives introduced by noise. Correspondingly, a Newton-Raphson-type algorithm is proposed to obtain the estimator, leading to a corrected likelihood estimator. To further enhance computational efficiency, we introduce a corrected least squares estimator based on the idea of bias correction. Theoretical analysis of both estimators is carefully conducted. Model generalizations and privacy protection enhancements are subsequently carefully discussed. The finite sample performances of different methods are demonstrated through extensive simulations. Based on collaboration with a third-party payment company and ensuring data confidentiality, we conducted an analysis of network effects between restaurants and interactions between restaurants and customers using the SAR and extended models.

 

Bio：伍书缘，上海财经大学统计与数据科学学院助理研究员，博士毕业于北京大学光华管理学院。主要研究领域包括联邦学习、分布式计算与统计优化算法等。在Journal of the Royal Statistical Society: Series B、Journal of Business and Economic Statistics、Journal of Computational and Graphical Statistics、Statistica Sinica等国际知名期刊上发表多篇学术论文。目前主持国家自然科学基金青年项目一项。