The Berry-Esseen bound for student's statistic
Open Access
- 1 January 1996
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 24 (1) , 491-503
- https://doi.org/10.1214/aop/1042644728
Abstract
. We prove the Berry-Esseen bound for the Student t-statistic. Underthe assumption of a third moment this bound coincide (up to an absolute constant)with the classical Berry-Esseen bound for the mean. In general the distributionof the Student statistic converges to the standard normal distribution function atleast as fast as the distribution of the mean, and sometimes faster. For example,rates of convergence can be proved if the underlying distribution is in the domainof attraction of the ...Keywords
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