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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.16978 |
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| _version_ | 1866911622047465472 |
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| author | Liu, Weiguang |
| author_facet | Liu, Weiguang |
| contents | We establish normal approximation in the Wasserstein metric for both non-degenerate and degenerate second-order U-statistics under cross-sectional dependence 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16978 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normal Approximation for U-Statistics with Cross-Sectional Dependence Liu, Weiguang Econometrics We establish normal approximation in the Wasserstein metric for both non-degenerate and degenerate second-order U-statistics under cross-sectional dependence 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. |
| title | Normal Approximation for U-Statistics with Cross-Sectional Dependence |
| topic | Econometrics |
| url | https://arxiv.org/abs/2411.16978 |