We propose employing a debiased-regularized, high-dimensional generalized method of moments (GMM) framework to perform inference on large-scale spatial panel networks. In particular, network structure with a flexible sparse deviation, which can be regarded either as latent or as misspecified from a predetermined adjacency matrix, is estimated using debiased machine learning approach. The theoretical analysis establishes the consistency and asymptotic normality of our proposed estimator, taking into account general temporal and spatial dependency inherent in the data-generating processes. The dimensionality allowance in presence of dependency is discussed. A primary contribution of our study is the development of uniform inference theory that enables hypothesis testing on the parameters of interest, including zero or non-zero elements in the network structure. Additionally, the asymptotic properties for the estimator are derived for both linear and nonlinear moments. Simulations demonstrate superior performance of our proposed approach. Lastly, we apply our methodology to investigate the spatial network effect of stock returns.

翻译：本文提出采用去偏正则化、高维广义矩估计（GMM）框架对大规模空间面板网络进行推断。特别地，我们将网络结构视为具有灵活稀疏偏差的模型，该偏差可被解释为潜在结构或来自预设邻接矩阵的错误设定，并通过去偏机器学习方法进行估计。理论分析建立了所提估计量的一致性和渐近正态性，同时考虑了数据生成过程中固有的时间与空间依赖性。本文讨论了存在依赖关系时的维度容许性。本研究的主要贡献在于发展了均匀推断理论，使得能够对感兴趣的参数（包括网络结构中的零元素或非零元素）进行假设检验。此外，针对线性和非线性矩条件，我们推导了估计量的渐近性质。模拟实验表明，所提方法具有优越性能。最后，我们将该方法应用于股票收益的空间网络效应研究。