🤖 AI Summary
This paper addresses limit theorems for random variables on network data, overcoming the conventional reliance on Euclidean or metric-space structures. It introduces a weak dependence modeling paradigm applicable to non-embeddable networks—such as financial and social networks—where node positions are unavailable or meaningless. Methodologically, it pioneers the generalization of functional (physical) dependence—originally developed for time series—to arbitrary network topologies, yielding a position-agnostic generalized weak dependence framework. Within this framework, the authors rigorously establish the law of large numbers and the central limit theorem for non-metric networks, and provide verifiable primitive conditions—for instance, dependence decay rates under spatial autoregressive models. The resulting concentration inequalities and limit theory constitute a universal and rigorous foundation for statistical inference on network-structured data.
📝 Abstract
This paper develops limit theorems for random variables with network dependence, without requiring that individuals in the network to be located in a Euclidean or metric space. This distinguishes our approach from most existing limit theorems in network econometrics, which are based on weak dependence concepts such as strong mixing, near-epoch dependence, and $ψ$-dependence. By relaxing the assumption of an underlying metric space, our theorems can be applied to a broader range of network data, including financial and social networks. To derive the limit theorems, we generalize the concept of functional dependence (also known as physical dependence) from time series to random variables with network dependence. Using this framework, we establish several inequalities, a law of large numbers, and central limit theorems. Furthermore, we verify the conditions for these limit theorems based on primitive assumptions for spatial autoregressive models, which are widely used in network data analysis.