arXiv 25 Nov 2024 · Econometrics
arXiv:2411.16978 · PDF · DOI · OpenAlex · Extracted main text
We establish normal approximation in the Wasserstein metric and central limit theorems for both non-degenerate and degenerate U-statistics with cross-sectionally dependent samples using Stein's method. For the non-degenerate case, our results extend recent studies on the asymptotic properties of sums of cross-sectionally dependent random variables. The degenerate case is more challenging due to the additional dependence induced by the nonlinearity of the U-statistic kernel. Through a specific implementation of Stein's method, we derive convergence rates under conditions on the mixing rate, the sparsity of the cross-sectional dependence structure, and the moments of the U-statistic kernel. Finally, we demonstrate the application of our theoretical results with a nonparametric specification test for data with cross-sectional dependence.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Fan, Yanqin and Li, Qi Central Limit Theorem for Degenerate U-statistics of Absolutely Regular Processes with Applications to Model Specification Testing | 1.000 | 5 | 3 | 100% |
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| 9 | Dehling, Herold and Wendler, Martin Central Limit Theorem and the Bootstrap for U-statistics of Strongly Mixing Data | 0.644 | 2 | 2 | 100% |
| 10 | de Jong, Peter A Central Limit Theorem for Generalized Quadratic Forms | 0.644 | 2 | 2 | 100% |
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