Wen Jiang, Yachen Wang, Zeqi Wu, Xingbai Xu
arXiv 22 Nov 2025 · Econometrics
arXiv:2511.17928 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Wu, Wei Biao (2005) Nonlinear system theory: Another look at dependence | 1.000 | 6 | 4 | 100% |
| 2 | Jenish, Nazgul and Prucha, Ingmar R (2012) On spatial processes and asymptotic inference under near-epoch dependence | 1.000 | 5 | 3 | 100% |
| 3 | Kojevnikov, Denis and Marmer, Vadim and Song, Kyungchul (2021) Limit theorems for network dependent random variables | 1.000 | 5 | 3 | 100% |
| 4 | Jenish, Nazgul and Prucha, Ingmar R (2009) Central limit theorems and uniform laws of large numbers for arrays of random fields | 0.928 | 4 | 3 | 100% |
| 5 | Wu, Zeqi and Jiang, Wen and Xu, Xingbai (2025) Applications of functional dependence to spatial econometrics self | 0.920 | 9 | 5 | 78% |
| 6 | Lee, Lung-fei and Yang, Chao and Yu, Jihai (2023) QML and efficient GMM estimation of spatial autoregressive models with dominant (popular) units | 0.909 | 8 | 4 | 75% |
| 7 | Xu, Xingbai and Lee, Lung-fei (2015) Maximum likelihood estimation of a spatial autoregressive Tobit model self | 0.874 | 9 | 5 | 67% |
| 8 | El Machkouri, Mohamed and Volný, Dalibor and Wu, Wei Biao (2013) A central limit theorem for stationary random fields | 0.843 | 3 | 3 | 100% |
| 9 | Xu, Xingbai and Lee, Lung-fei (2018) Sieve maximum likelihood estimation of the spatial autoregressive Tobit model self | 0.843 | 3 | 3 | 100% |
| 10 | Lee, Lung-fei (2004) Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models | 0.843 | 3 | 3 | 100% |
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