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Uniform Limit Theory for Network Data

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  • Yuya Sasaki

Abstract

I present a novel uniform law of large numbers (ULLN) for network-dependent data. While Kojevnikov, Marmer, and Song (KMS, 2021) provide a comprehensive suite of limit theorems and a robust variance estimator for network-dependent processes, their analysis focuses on pointwise convergence. On the other hand, uniform convergence is essential for nonlinear estimators such as M and GMM estimators (e.g., Newey and McFadden, 1994, Section 2). Building on KMS, I establish the ULLN under network dependence and demonstrate its utility by proving the consistency of both M and GMM estimators. A byproduct of this work is a novel maximal inequality for network data, which may prove useful for future research beyond the scope of this paper.

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  • Yuya Sasaki, 2025. "Uniform Limit Theory for Network Data," Papers 2503.00290, arXiv.org.
    • Handle: RePEc:arx:papers:2503.00290
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