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Testing network effects in weighted directed networks is a foundationalproblem in econometrics, sociology, and psychology. Yet, the prevalent edgedependency poses a significant methodological challenge. Most existing methodsare model-based and come with stringent assumptions, limiting theirapplicability. In response, we introduce a novel, fully nonparametric frameworkthat requires only minimal regularity assumptions. While inspired by recentdevelopments in $U$-statistic literature (arXiv:1712.00771, arXiv:2004.06615),our approach notably broadens their scopes. Specifically, we identified andcarefully addressed the challenge of indeterminate degeneracy in the teststatistics $-$ a problem that aforementioned tools do not handle. Weestablished Berry-Esseen type bound for the accuracy of type-I error ratecontrol. Using original analysis, we also proved the minimax optimality of ourtest's power. Simulations underscore the superiority of our method incomputation speed, accuracy, and numerical robustness compared to competingmethods. We also applied our method to the U.S. faculty hiring network data anddiscovered intriguing findings.

Optimal Nonparametric Inference on Network Effects with Dependent Edges