AI 中文总结
针对观测网络与真实交互网络可能不同的社会交互模型，提出网络调整广义矩估计（NA - GMM）方法，它能修改交互矩阵元素，避免无限制调整，证明了其对伪真实参数的一致性及渐近正态性，还有偏差减少特性，实证应用显示了该方法的有效性。
AI 中文摘要
本文针对观测网络可能与真实交互网络不同的社会交互模型，提出了一种网络调整广义矩估计（NA - GMM）方法。NA - GMM是一种新颖的惩罚广义矩方法，可修改观测交互矩阵元素以改善矩条件的拟合。为避免无限制的网络调整，该准则对调整量进行惩罚。NA - GMM一般收敛到伪真实参数。对于线性空间自回归模型，证明了NA - GMM估计量对伪真实参数是一致的，且在一般矩误设下渐近正态分布。还证明了固定权重版本的NA - GMM估计量相对于无网络调整的传统GMM具有理想的偏差减少特性。对美国县级新冠感染数据的实证应用证明了该方法的有效性。
英文摘要
This paper proposes a network-adjusted generalized method of moments (NA-GMM) estimator for social interaction models when the observed network may differ from the true interaction network. NA-GMM is a novel penalized GMM approach that allows the elements of the observed interaction matrix to be modified to improve the fit of the moment conditions. To avoid unrestricted network adjustments, the NA-GMM criterion introduces a penalty on the amount of adjustment. Since NA-GMM does not aim to estimate the true interaction network itself, the estimator generally converges to a pseudo-true parameter. For a linear spatial autoregressive model, we prove that the NA-GMM estimator is consistent for the pseudo-true parameter and is asymptotically normally distributed under general moment misspecification. We also prove that a fixed-weight version of the NA-GMM estimator has a desirable bias reduction property relative to conventional GMM without network adjustment. An empirical application to U.S. county-level COVID-19 infection data demonstrates the usefulness of the proposed method.
