A Note on Edgeworth Expansions for <Emphasis Type="Italic">U</Emphasis>-Statistics under Minimal Conditions |
| |
| Authors: | B-Y Jing W Zhou |
| |
| Institution: | (1) Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;(2) Department of Statistics and Applied Probability, National University of Singapore, 117546, Singapore |
| |
| Abstract: | A one-term Edgeworth expansion for U-statistics with kernel h(x, y) was derived by Jing and Wang 3] under optimal moment conditions. In this note, we show that one of the optimal moment conditions
E| h(X
1, X
2|5/3 < ∞ can be weakened to lim
t→∞
t
5/3
P(|h(X
1, X
2)| > t) → 0.
Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 453–440, July–September, 2005. |
| |
| Keywords: | U-statistics Edgeworth expansions optimal moments nonlattice condition |
| 本文献已被 SpringerLink 等数据库收录！ |
|
