An exponential nonuniform Berry-Esseen bound for self-normalized sums

Authors
Citation
Qy. Wang et By. Jing, An exponential nonuniform Berry-Esseen bound for self-normalized sums, ANN PROBAB, 27(4), 1999, pp. 2068-2088
Citations number
14
Categorie Soggetti
Mathematics
Journal title
ANNALS OF PROBABILITY
ISSN journal
00911798 → ACNP
Volume
27
Issue
4
Year of publication
1999
Pages
2068 - 2088
Database
ISI
SICI code
0091-1798(199910)27:4<2068:AENBBF>2.0.ZU;2-V
Abstract
In this paper we shall derive Exponential nonuniform Berry-Esseen bounds in the central limit theorem for self-normalized sums. We show that the size of the error can be reduced considerably by replacing the usual standardiza tion by self-normalization. Tn particular, we establish the exponential bou nds for the probability of the self-normalized sums under the condition tha t the third moment is finite, whereas an exponential moment assumption is r equired for the standardized sums. Applications to t-statistics and the pro babilities of moderate deviations of self-normalized sums are also discusse d.