This paper studies the estimation of network connectedness with focally sparse structure. We try to uncover the network effect with a flexible sparse deviation from a predetermined adjacency matrix. To be more specific, the sparse deviation structure can be regarded as latent or misspecified linkages. To obtain high-quality estimator for parameters of interest, we propose to use a double regularized high-dimensional generalized method of moments (GMM) framework. Moreover, this framework also facilitates us to conduct the inference. Theoretical results on consistency and asymptotic normality are provided with accounting for general spatial and temporal dependency of the underlying data generating processes. Simulations demonstrate good performance of our proposed procedure. Finally, we apply the methodology to study the spatial network effect of stock returns.

翻译：本文研究与核心分散结构的网络连接性的估计。 我们试图发现网络效应,与事先确定的相邻关系矩阵略有差异。 更具体地说,稀疏的偏差结构可被视为潜在或错误的关联。 为了获得有关参数的高质量估计符,我们提议使用一种双向的高度常规瞬时法(GMM)框架。此外,这个框架还便利我们进行推断。 关于一致性和无干扰性常态的理论结果,将基本数据生成过程的一般空间和时间依赖性考虑在内。模拟显示了我们拟议程序的良好表现。最后,我们采用这种方法来研究种群回报的空间网络效应。