On M-ancillarity

Abstract

The definition and properties are discussed of M -ancillarity, a concept introduced and studied first in an unpublished report and later by Bandorff-Nielsen (1973) and Barndorff-Nielsen & Kvist (1974). For simplicity attention is, in the main, restricted to finite discrete distributions. The principal new result is a technique for finding the M-ancillary statistics when the family of distributions is exponential of order 2.