A Central Limit Theorem for incomplete U-statistics over triangular arrays
Probability
2020-03-24 v1 Statistics Theory
Statistics Theory
Abstract
We analyze the fluctuations of incomplete -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. A possible application -- a CLT for the hitting time for random walk on random graphs -- will be presented in \cite{LoTe20b}
Cite
@article{arxiv.2003.10115,
title = {A Central Limit Theorem for incomplete U-statistics over triangular arrays},
author = {Matthias Löwe and Sara Terveer},
journal= {arXiv preprint arXiv:2003.10115},
year = {2020}
}