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Uniqueness of estimation and identifiability in mixture models
Author(s) -
Lindsay Bruce G.,
Roeder Kathryn
Publication year - 1993
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 - 10.2307/3315807
Subject(s) - mathematics , maximum likelihood , combinatorics , uniqueness , identifiability , estimator , mixing (physics) , humanities , calculus (dental) , statistics , mathematical analysis , physics , medicine , philosophy , dentistry , quantum mechanics
Abstract Further properties of the nonparametric maximum‐likelihood estimator of a mixing distribution are obtained by exploiting the properties of totally positive kernels. Sufficient conditions for uniqueness of the estimator are given. This result is more general, and the proof is substantially simpler, than given previously. When the component density has support on N points, it is shown that all identifiable mixing distributions have support on no more than N/2 points. Identifiable mixtures are shown to lie on the boundary of the mixture model space. The maximum‐likelihood estimate is shown to be unique if the vector of observations lies outside this space.