Standard Article

Ancillary Statistics

  1. N. Reid

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a15002

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Reid, N. 2005. Ancillary Statistics. Encyclopedia of Biostatistics. 1.

Author Information

  1. University of Toronto, Toronto, Ontario, Canada

Publication History

  1. Published Online: 15 JUL 2005

Abstract

An ancillary statistic is a function of the data whose distribution is free of the parameters in the model. Ancillary statistics are complementary in a certain sense to sufficient statistics. In the theory of statistics, it is often argued that inference should be conditional on ancillary statistics, when this is possible. Fisher showed that in a location model, the conditional distribution of the maximum likelihood estimator could be obtained by renormalizing the likelihood function, or, in other words, treating the likelihood function as a posterior distribution for the location parameter. This result has been generalized to provide an approximate conditional distribution to the maximum likelihood estimator, given an approximately ancillary statistic, a result known as the p* approximation.

Keywords:

  • asymptotic theory;
  • conditioning;
  • likelihood, location family;
  • parametric model;
  • p* approximation;
  • structural model