ON EXTERNAL ANCILLARITY

Abstract

Statistics distributed free of a certain parameter (called ancillary for the parameter) are of considerable use when sufficient estimation is not possible (Fisher (1925)). When the model involves, in addition to the parameters of interest, parameters not of direct interest (nuisance parameters) statistics which are distributed free of the latter may be of considerable use also. This requires a study of ancillary statistics which are not functions of the minimal sufficient statistic (MSS). In particular we study the general ancillary given in Williams (1982) and show that it has certain desirable properties including uniqueness under appropriate restrictions. Finally some non‐trivial applicat..