Standard Article

U-Statistics

  1. Paul Janssen

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a15172

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Janssen, P. 2005. U-Statistics. Encyclopedia of Biostatistics. 8.

Author Information

  1. Limburgs Universitair, Diepenbeek, Belgium

Publication History

  1. Published Online: 15 JUL 2005

Abstract

A U-statistic, calculated from a random sample of size n, is an average of a symmetric function of m sample values, calculated for all m-tuples in the sample. Examples are the sample variance, the Cramér-von Mises statistic of goodness of fit, and the Kaplan–Meier and Nelson–Aalen estimators in survival analysis. Asymptotic properties are described.

Keywords:

  • random sample;
  • sample variance;
  • Cramér-von Mises;
  • Kaplan–Meier;
  • Nelson–Aalen;
  • large samples;
  • bootstrap