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.
Publié le : 1988-07-14
Classification:
Central limit theorem,
rate of convergence,
sample variance,
studentizing,
60F05,
60G50
@article{1176991689,
author = {Hall, Peter},
title = {On the Effect of Random Norming on the Rate of Convergence in the Central Limit Theorem},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 1265-1280},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991689}
}
Hall, Peter. On the Effect of Random Norming on the Rate of Convergence in the Central Limit Theorem. Ann. Probab., Tome 16 (1988) no. 4, pp. 1265-1280. http://gdmltest.u-ga.fr/item/1176991689/