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ON EXTERNAL ANCILLARITY 1
Author(s) -
Lloyd C. J.
Publication year - 1985
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1985.tb00563.x
Subject(s) - sufficient statistic , nuisance parameter , statistic , uniqueness , mathematics , statistics , computer science , econometrics , estimator , mathematical analysis
summary 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 applications are given.