APPLICATIONS AND EXTENSIONS OF BASU'S RESULTS ON MAXIMAL ANCILLARITY

Maximality of ancillaries is important in both conditional inference without nuisance parameters and marginal inference with nuisance parameters. We extend results of Basu (1959) to the more classical former case and discuss the different nature of ancillaries in these two contexts. We apply the results to a general ancillary independent of a sufficient statistic. Finally, we discuss difficulties in finding necessary conditions for maximality.