A Multivariate CLT for Bounded Decomposable Random Vectors with the Best Known Rate

作者：Fang Xiao^*

来源：Journal of Theoretical Probability, 2016, 29(4): 1510-1523.

DOI：10.1007/s10959-015-0619-7

• Stein's method
• Multivariate normal approximation
• Non-smooth function distance
• Rate of convergence
• Random graph counting

We prove a multivariate central limit theorem with explicit error bound in a non-smooth function distance for sums of bounded decomposable -dimensional random vectors. The decomposition structure is similar to that of Barbour et al. (J Combin Theory Ser 47:125-145, 1989) and is more general than the local dependence structure considered in Chen and Shao (Ann Probab 32:1985-2028, 2004). The error bound is of the order , where is the dimension and is the number of summands. The dependence on , namely , is the best known dependence even for sums of independent and identically distributed random vectors, and the dependence on , namely , is optimal. We apply our main result to a random graph example.

• 出版日期2016-12