On the Effect of Random Norming on the Rate of Convergence in the Central Limit Theorem
Open Access
- 1 July 1988
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 16 (3) , 1265-1280
- https://doi.org/10.1214/aop/1176991689
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.Keywords
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