Abstract
We analyze the fluctuations of incomplete U-statistics over a triangular array of independent random variables. We give criteria for a Central Limit Theorem (CLT, for short) to hold in the sense that we prove that an appropriately scaled and centered version of the U-statistic converges to a normal random variable. Our method of proof relies on a martingale CLT. An application, a CLT for the hitting time for random walks on random graphs, will be presented in Löwe and Terveer (2020).
Acknowledgments
Research of both authors was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structur.
Citation
Matthias Löwe. Sara Terveer. "A Central Limit Theorem for incomplete U-statistics over triangular arrays." Braz. J. Probab. Stat. 35 (3) 499 - 522, August 2021. https://doi.org/10.1214/20-BJPS492
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