Optimal Nonparametric Inference on Network Effects with Dependent Edges
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916081825742848 |
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| author | Du, Wenqin Zhang, Yuan Zhou, Wen |
| author_facet | Du, Wenqin Zhang, Yuan Zhou, Wen |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_03072 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Nonparametric Inference on Network Effects with Dependent Edges Du, Wenqin Zhang, Yuan Zhou, Wen Methodology Statistics Theory 62E17, 62G10, 91D30 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. |
| title | Optimal Nonparametric Inference on Network Effects with Dependent Edges |
| topic | Methodology Statistics Theory 62E17, 62G10, 91D30 |
| url | https://arxiv.org/abs/2401.03072 |