Financial network analysis has gained significant attention recently. The identification, estimation, and inference issues are intrinsically important in understanding the underlying network structure. We try to uncover the network effect with a predetermined adjacency matrix, and in addition, we allow a flexible network specification by incorporating an unobserved network structure. In particular, the unobserved network structure can be regarded as latent or misclassified network linkages. To achieve a high-quality estimator for parameters in both components, we propose to estimate via a double regularized high dimensional GMM framework. Moreover, this framework also facilitates us to conduct the inference. The theory of consistency and asymptotic normality is provided with accounting for the general spatial and temporal dependency of the underlying data generating processes. Simulations demonstrate the good performance of our proposed estimation and inference procedure.
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