Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T15:27:46.129Z Has data issue: false hasContentIssue false
  • English
  • Français

Rates of convergence for U-Statistics with varying kernels

Published online by Cambridge University Press:  17 April 2009

N.C. Weber
N.C. Weber
Affiliation:
Department of Mathematical Statistics, University of Sydney, Sydney, New South Wales 2006, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Un be a U-statistic whose kernel depends on the size n of the sample under consideration. It is shown that when Un is suitably normalised its distribution function differs in Lp norm from the distribution function of a standard normal variable by a term of O(n-½).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1980 , pp. 1 - 5
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Callaert, Herman and Janssen, Paul, “The Berry-Esseen theorem for U-statistics”, Ann. Statist. 6 (1978), 417–421.Google Scholar
[2]Erickson, R.V., “On an Lp version of the Berry-Esseen theorem for independent and m-dependent variables”, Ann. Prob. 1 (1973), 497–503.CrossRefGoogle Scholar
[3]Erickson, R.V. and Koul, H.L., “L1 rates of convergence for linear rank statistics”, Ann. Statist. 4 (1976), 771–774.Google Scholar
[4]Kester, Adri, “Asymptotic normality of the number of small distances between random points in a cube”, Stochastic Process. Appl. 3 (1975), 45–54.Google Scholar
[5]Silverman, Bernard, Brown, Tim, “Short distances, flat triangles and Poisson limits”, J. Appl. Probab. 15 (1978), 815–825.Google Scholar