Open Access
August 2020 A refined Cramér-type moderate deviation for sums of local statistics
Xiao Fang, Li Luo, Qi-Man Shao
Bernoulli 26(3): 2319-2352 (August 2020). DOI: 10.3150/20-BEJ1195


We prove a refined Cramér-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 Erdős–Rényi random graph. To prove our main result, we develop exponential concentration inequalities and higher-order tail probability expansions via Stein’s method.


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Xiao Fang. Li Luo. Qi-Man Shao. "A refined Cramér-type moderate deviation for sums of local statistics." Bernoulli 26 (3) 2319 - 2352, August 2020.


Received: 1 August 2019; Revised: 1 January 2020; Published: August 2020
First available in Project Euclid: 27 April 2020

zbMATH: 07193962
MathSciNet: MR4091111
Digital Object Identifier: 10.3150/20-BEJ1195

Keywords: $k$-runs , Cramér-type moderate deviation , Erdős–Rényi random graph , local dependence , skewness correction , Stein’s method , U-statistic

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 3 • August 2020
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