## The Annals of Probability

- Ann. Probab.
- Volume 8, Number 6 (1980), 1037-1048.

### Characterizing the Rate of Convergence in the Central Limit Theorem

#### Abstract

Asymptotic upper and lower bounds are obtained for the uniform measure of the rate of convergence in the central limit theorem using a variety of norming constants. For many distributions the upper and lower bounds are of the same order of magnitude. As easy corollaries we deduce extensive generalizations of the classical characterizations of the rate of convergence in terms of series and order of magnitude conditions.

#### Article information

**Source**

Ann. Probab., Volume 8, Number 6 (1980), 1037-1048.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176994566

**Digital Object Identifier**

doi:10.1214/aop/1176994566

**Mathematical Reviews number (MathSciNet)**

MR602378

**Zentralblatt MATH identifier**

0456.60018

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 60G50: Sums of independent random variables; random walks

**Keywords**

Rate of convergence central limit theorem independent and identically distributed random variables

#### Citation

Hall, Peter. Characterizing the Rate of Convergence in the Central Limit Theorem. Ann. Probab. 8 (1980), no. 6, 1037--1048. doi:10.1214/aop/1176994566. https://projecteuclid.org/euclid.aop/1176994566