Bibliographic Details
| Title: |
Tail Bounds for the Suprema of Empirical Processes over Unbounded Classes of Functions. |
| Authors: |
Di Xin Zhang1 dixinz_23@sina.com |
| Superior Title: |
Acta Mathematica Sinica. Apr2006, Vol. 22 Issue 2, p339-346. 8p. |
| Subject Terms: |
*MATHEMATICAL functions, *DIFFERENTIAL equations, *MATHEMATICAL analysis, *MATHEMATICS, *PROBABILITY theory |
| Abstract: |
So far the study of exponential bounds of an empirical process has been restricted to a bounded index class of functions. The case of an unbounded index class of functions is now studied on the basis of a new symmetrization idea and a new method of truncating the original probability space; the exponential bounds of the tail probabilities for the supremum of the empirical process over an unbounded class of functions are obtained. The exponential bounds can be used to establish laws of the logarithm for the empirical processes over unbounded classes of functions. [ABSTRACT FROM AUTHOR] |
|
Copyright of Acta Mathematica Sinica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| Database: |
Academic Search Premier |