The Annals of Probability

Rates of Convergence in the Martingale Central Limit Theorem

Peter Hall and C. C. Heyde

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Abstract

We obtain a nonuniform estimate of the rate of convergence in the martingale central limit theorem for convergence to mixtures of normal distributions. The uniform rates of convergence obtained by several other authors are special cases of our nonuniform estimate. We also obtain a rate of convergence in B. M. Brown's central limit theorem, assuming only Brown's elementary conditions. This result is a martingale analogue of Feller's generalization of the Berry-Esseen theorem.

Article information

Source
Ann. Probab., Volume 9, Number 3 (1981), 395-404.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994413

Digital Object Identifier
doi:10.1214/aop/1176994413

Mathematical Reviews number (MathSciNet)
MR614625

Zentralblatt MATH identifier
0459.60042

JSTOR
links.jstor.org

Subjects
Primary: 60G42: Martingales with discrete parameter

Keywords
G0F05 Martingale central limit theorem mixtures of normal distributions nonuniform bound rate of convergence uniform bound

Citation

Hall, Peter; Heyde, C. C. Rates of Convergence in the Martingale Central Limit Theorem. Ann. Probab. 9 (1981), no. 3, 395--404. doi:10.1214/aop/1176994413. https://projecteuclid.org/euclid.aop/1176994413


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