ABSTRACT
In problems of parametric inference, an ancillary statistic is one whose distribution is the same for all parameter values. Ancillary statistics usually arise in one of two ways. The first and most common way in which an ancillary statistic occurs is as a random sample size or other random index identifying the experiment actually performed. The second type of ancillary arises in the context of a translation model or, more generally, a group transformation model. The examples demonstrate the poverty of any frequency theory of inference that ignores ancillary statistics. Having made that point, it must be stated that the difficulties involved in establishing a coherent frequency theory of conditional inference are formidable. Numerical computation of conditional distributions and conditional tail areas is often a complicated unappealing task. Approximation gives the conditional density of the maximum likelihood estimate of the canonical parameter corresponding to the transformation. On transforming to any other parameter, the form of the approximation remains the same.
