|
HKUST Institutional Repository >
Mathematics >
MATH Journal/Magazine Articles >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/1783.1/1787
|
| Title: | An exponential nonuniform Berry-Esseen bound for self-normalized sums |
| Authors: | Wang, Qiying
Jing, Bing-Yi |
| Keywords: | Berry-Esseen bound
Self-normalized sum
T-statistics
Moderate deviation
Nonuniform estimate |
| Issue Date: | Oct-1999 |
| Citation: | The annals of probability, 1999, v. 27, no. 4, p. 2068-2088 |
| 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 standardization by self-normalization. In particular, we establish the exponential bounds for the probability of the self-normalized sums under the condition that the third moment is finite, whereas an exponential moment assumption is required for the standardized sums. Applications to t-statistics and the probabilities of moderate deviations of self-normalized sums are also discussed. |
| Rights: | Published in Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics. |
| URI: | http://hdl.handle.net/1783.1/1787 |
| Appears in Collections: | MATH Journal/Magazine Articles
|
Files in This Item:
| File |
Description |
Size | Format |
|---|
| probability2068.pdf | | 1666Kb | Adobe PDF | View/Open |
|
Find published version via |
All items in this Repository are protected by copyright, with all rights reserved.
|
