A Central Limit Theorem for incomplete U-statistics over triangular\n arrays

2020/03/23 by Matthias Löwe, Sara Terveer, Löwe, Matthias +1
Mathematics · #60F05 #62G05 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2003.10115

openalex publication_date 2020/03/23 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We analyze the fluctuations of incomplete U-statistics over a triangular\narray of independent random variables. We give criteria for a Central Limit\nTheorem (CLT, for short) to hold in the sense that we prove that an\nappropriately scaled and centered version of the U-statistic converges to a\nnormal random variable. Our method of proof relies on a martingale CLT. A\npossible application -- a CLT for the hitting time for random walk on random\ngraphs -- will be presented in citeLoTe20b\n

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