Published Online: 15 JUL 2005
Copyright © 2005 John Wiley & Sons, Ltd
Encyclopedia of Biostatistics
How to Cite
Reid, N. 2005. Ancillary Statistics. Encyclopedia of Biostatistics.
- Published Online: 15 JUL 2005
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.
- asymptotic theory;
- likelihood, location family;
- parametric model;
- p* approximation;
- structural model