Non-uniform Berry–Esseen Bounds for Weighted U-Statistics and Generalized L-Statistics

Haojun Hu , Qi-Man Shao

Communications in Mathematics and Statistics ›› 2013, Vol. 1 ›› Issue (3) : 351 -367.

PDF
Communications in Mathematics and Statistics ›› 2013, Vol. 1 ›› Issue (3) : 351 -367. DOI: 10.1007/s40304-013-0019-1
Article

Non-uniform Berry–Esseen Bounds for Weighted U-Statistics and Generalized L-Statistics

Author information +
History +
PDF

Abstract

Weighted U-statistics and generalized L-statistics are commonly used in statistical inference and their asymptotic properties have been well developed. In this paper sharp non-uniform Berry–Esseen bounds for weighted U-statistics and generalized L-statistic are established.

Keywords

Weighted U-statistics / Generalized L-statistic / L-statistic / U-statistic / Non-uniform Berry–Esseen bound / Normal approximation

Cite this article

Download citation ▾
Haojun Hu, Qi-Man Shao. Non-uniform Berry–Esseen Bounds for Weighted U-Statistics and Generalized L-Statistics. Communications in Mathematics and Statistics, 2013, 1(3): 351-367 DOI:10.1007/s40304-013-0019-1

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Borovshikh Y.V., Weber N.C. Asymptotic distributions for a class of generalized L-statistics. Bernoulli. 2010, 16 1177-1190

[2]

Cai Z.W. Moderate deviations and large deviations of generalized L-statistics. Chin. Ann. Math., Ser. A. 1992, 13 364-372

[3]

Chen L.H.Y., Goldstein L., Shao Q.M. Normal Approximation by Stein’s Method. 2011 Heidelberg: Springer

[4]

Chen L.H.Y., Shao Q.M. Normal approximation for nonlinear statistics using a concentration inequality approach. Bernoulli. 2007, 13 581-599

[5]

Helmers R., Janssen P., Serfling R.J. Berry–Esseen bound and bootstrap results for generalized L-statistics. Scand. J. Stat.. 1990, 17 65-77

[6]

Helmers R., Ruymgaart F.H. Asymptotic normality of generalized L-statistics with unbounded scores. J. Stat. Plan. Inference. 1988, 19 43-53

[7]

Major P. Asymptotic distributions for weighted U-statistics. Ann. Probab.. 1994, 22 1514-1535

[8]

O’Neil K.A., Redner R.A. Asymptotic distributions of weighted U-statistics of degree two. Ann. Probab.. 1993, 21 1159-1169

[9]

Rifi M., Utzet F. On the asymptotic behavior of weighted U-statistics. J. Theor. Probab.. 2000, 13 141-167

[10]

Shapiro C.P., Hubert L. Asymptotic normality of permutation statistics derived from weighted sums of bivariate functions. Ann. Stat.. 1979, 7 788-794

[11]

Serfling R. Approximation Theorems of Mathematical Statistics. 1980 New York: Wiley

[12]

Serfling R. Generalized L-, M- and R-statistics. Ann. Stat.. 1984, 12 76-86

[13]

Serfling R. Robust estimation via generalized L-statistics: theory, applications, and perspectives. Advances on Methodological and Applied Aspects of Probability and Statistics. 1998 London: Taylor & Francis. 197-217

AI Summary AI Mindmap
PDF

166

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/