On the constant in the nonuniform version of the Berry-Esseen theorem
In 2001, Chen and Shao gave the nonuniform estimation of the rate of convergence in Berry-Esseen theorem for independent random variables via Stein-Chen-Shao method. The aim of this paper is to obtain a constant in Chen-Shao theorem, where the random variables are not necessarily identically distrib...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1951 |
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| _version_ | 1832561408892469248 |
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| author | K. Neammanee |
| author_facet | K. Neammanee |
| author_sort | K. Neammanee |
| collection | DOAJ |
| description | In 2001, Chen and Shao gave the nonuniform estimation of the rate
of convergence in Berry-Esseen theorem for independent random
variables via Stein-Chen-Shao method. The aim of this paper is to
obtain a constant in Chen-Shao theorem, where the random variables
are not necessarily identically distributed and the
existence of their third moments are not assumed. The bound is
given in terms of truncated moments and the constant obtained is
21.44 for most values. We use a technique called Stein's method,
in particular the Chen-Shao concentration inequality. |
| format | Article |
| id | doaj-art-1972e12d75b643009e6e3db07d64c434 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1972e12d75b643009e6e3db07d64c4342025-02-03T01:25:03ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005121951196710.1155/IJMMS.2005.1951On the constant in the nonuniform version of the Berry-Esseen theoremK. Neammanee0Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, ThailandIn 2001, Chen and Shao gave the nonuniform estimation of the rate of convergence in Berry-Esseen theorem for independent random variables via Stein-Chen-Shao method. The aim of this paper is to obtain a constant in Chen-Shao theorem, where the random variables are not necessarily identically distributed and the existence of their third moments are not assumed. The bound is given in terms of truncated moments and the constant obtained is 21.44 for most values. We use a technique called Stein's method, in particular the Chen-Shao concentration inequality.http://dx.doi.org/10.1155/IJMMS.2005.1951 |
| spellingShingle | K. Neammanee On the constant in the nonuniform version of the Berry-Esseen theorem International Journal of Mathematics and Mathematical Sciences |
| title | On the constant in the nonuniform version of the Berry-Esseen theorem |
| title_full | On the constant in the nonuniform version of the Berry-Esseen theorem |
| title_fullStr | On the constant in the nonuniform version of the Berry-Esseen theorem |
| title_full_unstemmed | On the constant in the nonuniform version of the Berry-Esseen theorem |
| title_short | On the constant in the nonuniform version of the Berry-Esseen theorem |
| title_sort | on the constant in the nonuniform version of the berry esseen theorem |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1951 |
| work_keys_str_mv | AT kneammanee ontheconstantinthenonuniformversionoftheberryesseentheorem |