Speeds of Convergence and Asymptotic Expansions in the Central Limit Theorem: A Treatment by Operators

Abstract

Speeds of convergence to normality and asymptotic expansions for sums of independent random vectors in $\mathbb{R}^k, k \geqslant 1$ are investigated using the method of operators. Existing results are improved and some new results obtained. In particular, asymptotic expansions for smooth functions are derived.