## The Annals of Probability

- Ann. Probab.
- Volume 10, Number 4 (1982), 1004-1018.

### Bounds on the Rate of Convergence of Moments in the Central Limit Theorem

#### Abstract

We derive two-sided bounds on the rate of convergence of moments in the central limit theorem. A variety of norming constants is considered, and it is shown that a very delicate alteration to these constants can have a significant effect on the rate. Indeed, the influence of norming constants on rates of convergence of moments is of a more subtle nature than in the central limit theorem itself. We present several examples to illustrate some extreme cases.

#### Article information

**Source**

Ann. Probab., Volume 10, Number 4 (1982), 1004-1018.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993721

**Digital Object Identifier**

doi:10.1214/aop/1176993721

**Mathematical Reviews number (MathSciNet)**

MR672300

**Zentralblatt MATH identifier**

0516.60025

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

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

**Keywords**

Central limit theorem moments norming constants rates of convergence

#### Citation

Hall, Peter. Bounds on the Rate of Convergence of Moments in the Central Limit Theorem. Ann. Probab. 10 (1982), no. 4, 1004--1018. doi:10.1214/aop/1176993721. https://projecteuclid.org/euclid.aop/1176993721