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