Journal ArticleDOI
Mixture Models, Outliers, and the EM Algorithm
TLDR
The EM algorithm provides a simple and easily programmed iterative solution for the ML estimates of the parameters in the models to identify outliers in single sample or regression problems, based on mixture models.Abstract:
Maximum likelihood (ML) methods are described for the identification of outliers in single sample or regression problems, based on mixture models. The EM algorithm provides a simple and easily programmed iterative solution for the ML estimates of the parameters in the models. The procedure is illustrated on three examples.read more
Citations
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Journal ArticleDOI
An entropy criterion for assessing the number of clusters in a mixture model
Gilles Celeux,Gilda Soromenho +1 more
TL;DR: In this article, an entropy criterion is proposed to estimate the number of clusters arising from a mixture model, which is derived from a relation linking the likelihood and the classification likelihood of a mixture.
Journal ArticleDOI
Switching regression models and fuzzy clustering
TL;DR: A family of objective functions called fuzzy c-regression models, which can be used too fit switching regression models to certain types of mixed data, is presented and a general optimization approach is given and corresponding theoretical convergence results are discussed.
Journal ArticleDOI
A general maximum likelihood analysis of variance components in generalized linear models.
TL;DR: An EM algorithm for nonparametric maximum likelihood (ML) estimation in generalized linear models with variance component structure is described and a simple method is described for obtaining correct standard errors for parameter estimates when using the EM algorithm.
Journal ArticleDOI
Estimation and Hypothesis Testing in Finite Mixture Models
Murray Aitkin,Donald B. Rubin +1 more
TL;DR: In this article, a prior distribution on X and estimates 0 by maximizing the likelihood of the data given 0 with X integrated out is used to test the likelihood ratio of the underlying densities.
Journal ArticleDOI
Location of Several Outliers in Multiple-Regression Data Using Elemental Sets
TL;DR: In this paper, the authors proposed two summary statistics: an unweighted median and a weighted median, which are more efficient but less robust than the weighted median and the unweighting median, respectively.
References
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Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Book
Outliers in Statistical Data
Vic Barnett,Toby Lewis +1 more
TL;DR: In this article, the authors present an updated version of the reference work on outliers, including new areas of study such as outliers in direction data as well as developments in fields such as discordancy tests for univariate and multivariate samples.
Journal ArticleDOI