Inferential and geometric structures

Abstract

Let t be a sufficient statistic for the parametric model M with model function p(x;ω), and let (s,a) be a one-to-one transformation of t such that (i) s is of the same dimension as the parameter 4), i.e. dimension d (ii) a is distribution constant, either exactly or approximately. We then say that a is an ancillary statistic, or an ancillary for brevity. This extends the definition given in section 1.5 which was for the case s = $\hat{\omega }$. Furthermore, we call (s,a) a conditionality structure. The partition of the range space T of t generated by a is termed the ancillary foliation and in case s equals the maximum likelihood estimator $\hat{\omega }$ the partition of T determined by $\hat{\omega }$ is called the maximum likelihood foliation.