A refined Cramér-type moderate deviation for sums of local statistics

Xiao Fang; Li Luo; Qi Man Shao

doi:10.3150/20-BEJ1195

A refined Cramér-type moderate deviation for sums of local statistics

Xiao Fang, Li Luo, Qi Man Shao

Research output: Contribution to journal › Journal Article › peer-review

14 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2319-2352
Number of pages	34
Journal	Bernoulli
Volume	26
Issue number	3
DOIs	https://doi.org/10.3150/20-BEJ1195
Publication status	Published - Aug 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020 ISI/BS

Keywords

Cramér-type moderate deviation
Erdős-Rényi random graph
K-runs
Local dependence
Skewness correction
Stein's method
U-statistic

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10.3150/20-BEJ1195

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title = "A refined Cram{\'e}r-type moderate deviation for sums of local statistics",

abstract = "We prove a refined Cram{\'e}r-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{\H o}s-R{\'e}nyi random graph. To prove our main result, we develop exponential concentration inequalities and higher-order tail probability expansions via Stein's method.",

keywords = "Cram{\'e}r-type moderate deviation, Erd{\H o}s-R{\'e}nyi random graph, K-runs, Local dependence, Skewness correction, Stein's method, U-statistic",

author = "Xiao Fang and Li Luo and Shao, \{Qi Man\}",

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year = "2020",

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T1 - A refined Cramér-type moderate deviation for sums of local statistics

AU - Fang, Xiao

AU - Luo, Li

AU - Shao, Qi Man

PY - 2020/8

Y1 - 2020/8

N2 - 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.

AB - 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.

KW - Cramér-type moderate deviation

KW - Erdős-Rényi random graph

KW - K-runs

KW - Local dependence

KW - Skewness correction

KW - Stein's method

KW - U-statistic

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:000530027600026

UR - https://www.scopus.com/pages/publications/85091158314

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DO - 10.3150/20-BEJ1195

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VL - 26

SP - 2319

EP - 2352

JO - Bernoulli

JF - Bernoulli

IS - 3

ER -

A refined Cramér-type moderate deviation for sums of local statistics

Abstract

Bibliographical note

Keywords

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