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Likelihood Estimation with Normal Mixture Models
Author(s) -
Basford K. E.,
McLachlan G. J.
Publication year - 1985
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347474
Subject(s) - homoscedasticity , heteroscedasticity , mathematics , mixture model , maximum likelihood , context (archaeology) , multivariate normal distribution , maximum likelihood sequence estimation , statistics , restricted maximum likelihood , covariance , quasi maximum likelihood , estimator , expectation–maximization algorithm , likelihood ratio test , econometrics , likelihood function , multivariate statistics , paleontology , biology
SUMMARY We consider some of the problems associated with likelihood estimation in the context of a mixture of multivariate normal distributions. Unfortunately with mixture models, the likelihood equation usually has multiple roots and so there is the question of which root to choose. In the case of equal covariance matrices the choice of root is straightforward in the sense that the maximum likelihood estimator exists and is consistent. However, an example is presented to demonstrate that the adoption of a homoscedastic normal model in the presence of some heteroscedasticity can considerably influence the likelihood estimates, in particular of the mixing proportions, and hence the consequent clustering of the sample at hand.