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Sufficient Statistic

  1. William E. Strawderman

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a15162

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Strawderman, W. E. 2005. Sufficient Statistic. Encyclopedia of Biostatistics. 8.

Author Information

  1. Rutgers University, Piscataway, NJ, USA

Publication History

  1. Published Online: 15 JUL 2005


A sufficient statistic is such that the conditional distribution of the data given the sufficient statistic does not depend on any unknown parameters. In this sense, it contains all the information in the original data. A necessary and sufficient condition is the factorization theorem. A minimal sufficient statistic is a function of every other sufficient statistic, and is conveniently found for distributions in the exponential family. Topics described here include complete sufficient statistics, minimum variance estimation, uniformly most powerful unbiased tests, Bayesian methods, and invariance.


  • conditional;
  • factorization;
  • minimal sufficient;
  • exponential family;
  • complete sufficient;
  • Rao–Blackwell;
  • minimum variance;
  • UMPU test;
  • Neyman structure;
  • Bayesian;
  • invariance