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Mixtures, embedding, and ancillarity
Author(s) -
Evans M.,
Fraser D. A. S.,
Monette G.
Publication year - 1985
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315161
Subject(s) - mathematics , embedding , transformation (genetics) , combinatorics , humanities , mathematical economics , statistics , philosophy , computer science , artificial intelligence , biochemistry , chemistry , gene
Ancillary statistics, proposed by Fisher (1925), can be constructed by forming a mixture model (Birnbaum 1962) or can be extracted or derived from a transformation‐parameter model (Peisakoff 1951, Fraser 1961) or from the corresponding error‐based structural model (Fraser 1968, 1979); these latter models involve an implicit mixture structure. Compound models with ancillaries can also be formed by a cross embedding , discussed from a technical viewpoint in this paper. Of the 25 examples in Buehler (1982), 22 are mixtures or implicit mixtures and 3 correspond to cross embedding. The cross embedding examples exemplify the nonuniqueness difficulties with ancillaries. This paper discusses a simple and two generalized versions of cross embedding but makes no general valuations of these for statistical inference; their role within inference is discussed in Evans, Fraser, and Monette (1984, 1985).