A multivariate CLT for bounded decomposable random vectors with the best known rate

2014/08/03 by Xiao Fang, Fang, Xiao
Decision Sciences · Mathematics · #60F05 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1408.0508

openalex publication_date 2014/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a multivariate central limit theorem with explicit error bound on a non-smooth function distance for sums of bounded decomposable d-dimensional random vectors. The decomposition structure is similar to that of Barbour, Karoński and Ruciński (1989) and is more general than the local dependence structure considered in Chen and Shao (2004). The error bound is of the order d^(1)/(4) n^-(1)/(2), where d is the dimension and n is the number of summands. The dependence on d, namely d^(1)/(4), is the best known dependence even for sums of independent and identically distributed random vectors, and the dependence on n, namely n^-(1)/(2), is optimal. We apply our main result to a random graph example.

Citations

• Stein couplings for normal approximation

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