## The Annals of Probability

- Ann. Probab.
- Volume 5, Number 1 (1977), 28-41.

### 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.

#### Article information

**Source**

Ann. Probab., Volume 5, Number 1 (1977), 28-41.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176995888

**Digital Object Identifier**

doi:10.1214/aop/1176995888

**Mathematical Reviews number (MathSciNet)**

MR428400

**Zentralblatt MATH identifier**

0362.60041

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

**Keywords**

Multidimensional central limit theorem speeds of convergence

#### Citation

Sweeting, T. J. Speeds of Convergence for the Multidimensional Central Limit Theorem. Ann. Probab. 5 (1977), no. 1, 28--41. doi:10.1214/aop/1176995888. https://projecteuclid.org/euclid.aop/1176995888