2021/12/21 by Songhao Liu, Liu, Song-Hao, Zhuo-Song Zhang +1
Computer Science · Decision Sciences · Mathematics · #60F10 60F05 #Cryptography and Data Security #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2112.10946
openalex publication_date 2021/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish Cramér-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are obtained. Our main results are more general or shaper than the existing results in the literature. The main results follows from a more general Cramér-type moderate deviation theorem for dependent random variables without any boundedness assumptions, which is of independent interest. The proofs couple Stein's method with a recursive argument.