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Normal Approximation for U-Statistics with Cross-Sectional Dependence

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  • Weiguang Liu

Abstract

We apply Stein's method to investigate the normal approximation for both non-degenerate and degenerate U-statistics with cross-sectionally dependent underlying processes in the Wasserstein metric. We show that the convergence rates depend on the mixing rates, the sparsity of the cross-sectional dependence, and the moments of the kernel functions. Conditions are derived for central limit theorems to hold as corollaries. We demonstrate one application of the theoretical results with nonparametric specification test for data with cross-sectional dependence.

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  • Weiguang Liu, 2024. "Normal Approximation for U-Statistics with Cross-Sectional Dependence," Papers 2411.16978, arXiv.org.
    • Handle: RePEc:arx:papers:2411.16978
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    3. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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