Testing network effects in weighted directed networks is a foundational problem in econometrics, sociology, and psychology. Yet, the prevalent edge dependency poses a significant methodological challenge. Most existing methods are model-based and come with stringent assumptions, limiting their applicability. In response, we introduce a novel, fully nonparametric framework that requires only minimal regularity assumptions. While inspired by recent developments in $U$-statistic literature (arXiv:1712.00771, arXiv:2004.06615), our approach notably broadens their scopes. Specifically, we identified and carefully addressed the challenge of indeterminate degeneracy in the test statistics $-$ a problem that aforementioned tools do not handle. We established Berry-Esseen type bound for the accuracy of type-I error rate control. Using original analysis, we also proved the minimax optimality of our test's power. Simulations underscore the superiority of our method in computation speed, accuracy, and numerical robustness compared to competing methods. We also applied our method to the U.S. faculty hiring network data and discovered intriguing findings.

翻译：在加权有向网络中检验网络效应是计量经济学、社会学和心理学中的基础问题。然而，普遍存在的边缘依赖性构成了重大的方法论挑战。现有方法大多基于模型并带有严格假设，限制了其适用性。为此，我们引入了一种全新的完全非参数框架，仅需极少的正则性假设。虽然受近期U统计量文献（arXiv:1712.00771、arXiv:2004.06615）进展的启发，但我们的方法显著扩展了其适用范围。具体而言，我们识别并审慎解决了检验统计量中不确定退化性这一挑战——上述工具未能处理该问题。我们建立了I类错误率控制精度的Berry-Esseen型界限。通过原创性分析，我们还证明了检验功效的极小化最优性。数值模拟表明，与竞争方法相比，本方法在计算速度、准确性和数值稳健性方面均具有优越性。我们将该方法应用于美国教职招聘网络数据，发现了令人瞩目的结果。