Skewness correction in tail probability approximations for sums of local statistics

Xiao Fang; Li Luo; Qi-Man Shao

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arXiv · 1904.02623

Skewness correction in tail probability approximations for sums of local statistics

Xiao Fang·Li Luo·Qi-Man Shao

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Abstract

Correcting for skewness can result in more accurate tail probability approximations in the central limit theorem for sums of independent random variables. In this paper, we extend the theory to sums of local statistics of independent random variables and apply the result to $k$-runs, U-statistics, and subgraph counts in the Erdös-Rényi random graph. To prove our main result, we develop exponential concentration inequalities and higher-order Cramér-type moderate deviations via Stein's method.

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BibTeX RIS

Xiao Fang, Li Luo, Qi-Man Shao. 2019-04-04. Skewness correction in tail probability approximations for sums of local statistics. https://arxiv.org/abs/1904.02623

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