## The Annals of Probability

- Ann. Probab.
- Volume 16, Number 3 (1988), 1265-1280.

### On the Effect of Random Norming on the Rate of Convergence in the Central Limit Theorem

#### Abstract

It is shown that "studentizing," i.e., normalizing by the sample standard deviation rather than the population standard deviation, can improve the rate of convergence in the central limit theorem. This provides concise confirmation of one feature of the folklore that a studentized sum is in some sense more robust than a normed sum. The case of infinite population standard deviation is also examined.

#### Article information

**Source**

Ann. Probab., Volume 16, Number 3 (1988), 1265-1280.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176991689

**Digital Object Identifier**

doi:10.1214/aop/1176991689

**Mathematical Reviews number (MathSciNet)**

MR942767

**Zentralblatt MATH identifier**

0687.60021

**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 rate of convergence sample variance studentizing

#### Citation

Hall, Peter. On the Effect of Random Norming on the Rate of Convergence in the Central Limit Theorem. Ann. Probab. 16 (1988), no. 3, 1265--1280. doi:10.1214/aop/1176991689. https://projecteuclid.org/euclid.aop/1176991689