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
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.
Ann. Probab., Volume 16, Number 3 (1988), 1265-1280.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G50: Sums of independent random variables; random walks
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