Speeds of Convergence for the Multidimensional Central Limit Theorem

Abstract

Speeds of convergence to normality for sums of independent and identically distributed random vectors in $\mathbb{R}^k, k \geqq 1$, are investigated using the method of operators. Results obtained improve and extend existing results on speeds of convergence for the expectations of both bounded and certain unbounded Borel measurable functions, and nonuniform convergence rates.