Free Access
Issue |
ESAIM: PS
Volume 15, 2011
|
|
---|---|---|
Page(s) | 168 - 179 | |
DOI | https://doi.org/10.1051/ps/2009014 | |
Published online | 05 January 2012 |
- I.B. Alberink and V. Bentkus, Berry-Esseen bounds for von-Mises and U-statistics. Lith. Math. J. 41 (2001) 1–16. [CrossRef] [Google Scholar]
- I.B. Alberink and V. Bentkus, Lyapunov type bounds for U-statistics. Theory Probab. Appl. 46 (2002) 571–588. [CrossRef] [Google Scholar]
- J.N. Arvesen, Jackknifing U-statistics. Ann. Math. Statist. 40 (1969) 2076–2100. [CrossRef] [MathSciNet] [Google Scholar]
- Y.V. Borovskikh and N.C. Weber, Large deviations of U-statistics I. Lietuvos Matematikos Rinkinys 43 (2003) 13–37. [Google Scholar]
- Y.V. Borovskikh and N.C. Weber, Large deviations of U-statistics I. Lietuvos Matematikos Rinkinys 43 (2003) 294–316. [Google Scholar]
- H. Callaert and N. Veraverbeke, The order of the normal approximation for a studentized U-statistics. Ann. Statist. 9 (1981) 194–200. [CrossRef] [MathSciNet] [Google Scholar]
- W. Hoeffding, A class of statistics with asymptotically normal distribution. Ann. Math. Statist. 19 (1948) 293–325. [Google Scholar]
- B.-Y. Jing, Q.M. Shao and Q. Wang, Self-normalized Cramér-type large deviation for independent random variables. Ann. Probab. 31 (2003) 2167–2215. [CrossRef] [MathSciNet] [Google Scholar]
- B.-Y. Jing, Q.M. Shao, W. Zhou, Saddlepoint approximation for Student's t-statistic with no moment conditions. Ann. Statist. 32 (2004) 2679–2711. [CrossRef] [MathSciNet] [Google Scholar]
- V.S. Koroljuk and V. Yu. Borovskich, Theory of U-statistics. Kluwer Academic Publishers, Dordrecht (1994). [Google Scholar]
- Q.M. Shao, Self-normalized large deviations. Ann. Probab. 25 (1997) 285–328. [CrossRef] [MathSciNet] [Google Scholar]
- Q.M. Shao, Cramér-type large deviation for Student's t statistic. J. Theorect. Probab. 12 (1999) 387–398. [Google Scholar]
- V.H. De La Pena, M.J. Klass and T.L. Lai, Self-normalized processes: exponential inequalities, moment bound and iterated logarithm laws. Ann. Probab. 32 (2004) 1902–1933. [CrossRef] [MathSciNet] [Google Scholar]
- M. Vardemaele and N. Veraverbeke, Cramer type large deviations for studentized U-statistics. Metrika 32 (1985) 165–180. [CrossRef] [Google Scholar]
- Q. Wang, Bernstein type inequalities for degenerate U-statistics with applications. Ann. Math. Ser. B 19 (1998) 157–166. [Google Scholar]
- Q. Wang, B.-Y. Jing and L. Zhao, The Berry-Esséen bound for studentized statistics. Ann. Probab. 28 (2000) 511–535. [CrossRef] [MathSciNet] [Google Scholar]
- Q. Wang and N.C. Weber, Exact convergence rate and leading term in the central limit theorem for U-statistics. Statist. Sinica 16 (2006) 1409–1422. [MathSciNet] [Google Scholar]
- L. Zhao, The rate of the normal approximation for a studentized U-statistic. Science Exploration 3 (1983) 45–52. [MathSciNet] [Google Scholar]
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