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A Comment on Maximum Likelihood Estimation for Finite Mixtures of Distributions
Author(s) -
Burnham K. P.
Publication year - 1988
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710300318
Subject(s) - mathematics , exponential family , maximum likelihood , parametric statistics , expectation–maximization algorithm , dimensionality reduction , curse of dimensionality , exponential function , mixture model , estimation , component (thermodynamics) , statistics , computer science , mathematical analysis , physics , artificial intelligence , thermodynamics , management , economics
Iterative numerical methods are necessary to find the maximum likelihood estimates for finite mixture distributions. This paper shows that it will often be possible to analytically reduce the number of equations that must ultimately be solved numerically. Such a reduction in dimensionality has not generally been used, or sought after, for mixture distributions. Yet such results are easily derived when each mixture component is assumed to be from the same parametric model within the exponential family.