Limit Theorems for Network Dependent Random Variables

Denis Kojevnikov, Vadim Marmer () and Kyungchul Song

Papers from arXiv.org

Abstract: This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly transformed variables. We provide a law of large numbers and central limit theorem for network dependent variables. We also provide a method of calculating standard errors robust to general forms of network dependence. For that purpose, we rely on a network heteroskedasticity and autocorrelation consistent (HAC) variance estimator, and show its consistency. The results rely on conditions characterized by tradeoffs between the rate of decay of dependence across a network and network's denseness. Our approach can accommodate data generated by network formation models, random fields on graphs, conditional dependency graphs, and large functional-causal systems of equations.

Date: 2019-03, Revised 2021-02
New Economics Papers: this item is included in nep-ecm
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Published in Journal of Econometrics, 222(2), June 2021, 882-908

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http://arxiv.org/pdf/1903.01059 Latest version (application/pdf)

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Journal Article: Limit theorems for network dependent random variables (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1903.01059

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