Bias-Correction for Privacy-Protected Spatial Autoregressive Models with Application to Restaurant Network Analysis
隐私保护空间自回归模型的偏差校正与餐馆网络应用AI 解读 ↓
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隐私保护空间自回归模型的偏差校正与餐馆网络应用
- 研究问题
- 当隐私保护同时向结果和协变量加入噪声时，如何估计空间自回归模型的网络效应，克服传统准极大似然难以直接实施的问题？
- 方法与思路
- 作者从忽略协变量噪声的伪似然出发，提出同时校正两类噪声的 Newton–Raphson 型算法，并另设偏差校正最小二乘估计。
- 材料陈述的贡献
- 摘要称，所提估计在适当条件下一致且渐近正态；餐馆交易应用发现显著竞争性网络效应，并揭示餐馆与顾客的互动模式。
- 阅读关注点
- 应核对隐私噪声的分布与已知信息、网络权重矩阵设定、偏差修正推导，以及应用中竞争性效应的统计与经济解释。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未说明具体隐私机制和正则条件，显著网络系数也不足以单独确立因果关系。
原文摘要
Spatial autoregressive (SAR) models and their extensions are important tools for studying network effects. However, with an increasing emphasis on data privacy, data providers often implement protection measures that render standard SAR models inapplicable. In this study, we introduce a privacy-protected SAR model that incorporates noise into both the response and covariates to meet privacy requirements. With noise present in both components, the traditional quasi-maximum likelihood estimator becomes difficult to compute because the likelihood function cannot be directly formulated. To bypass this hurdle, we begin with a pseudo-likelihood approach, initially omitting the noise in the covariates. A Newton-Raphson algorithm is then applied to compute the estimator; however, the estimator is biased. To address this, we propose a bias-corrected Newton-Raphson-type algorithm that simultaneously accounts for noise in both the response and covariates. We further show, under appropriate regularity conditions, that the resulting estimator is consistent and asymptotically normal. To further enhance computational efficiency, we also develop a bias-corrected least squares estimator. Several extensions are discussed, and the finite-sample performance of the proposed methods is evaluated through extensive simulations. We apply the proposed methodology to restaurant transaction data from a third-party payment platform. Our method identifies a statistically significant competitive network effect among restaurants and further reveals meaningful restaurant-customer interaction patterns.