A Refined Cramer-Type Moderate Deviation for Sums of Local Statistics
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AbstractWe prove a refined Cram\'er-type moderate deviation result by taking into account of the skewness in normal approximation for sums of local statistics of independent random variables. We apply the main result to $k$-runs, U-statistics, and subgraph counts in the Erd\"os-R\'enyi random graph. To prove our main result, we develop exponential concentration inequalities and higher-order tail probability expansions via Stein's method.
Acceptance Date07/01/2020
All Author(s) ListXiao Fang, Li Luo, Qi-Man Shao
Journal nameBernoulli
Volume Number26
Issue Number3
Pages2319 - 2352
LanguagesEnglish-United States

Last updated on 2020-19-10 at 00:44