On EM algorithms and their proximal generalizations
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 308-326.

In this paper, we analyze the celebrated EM algorithm from the point of view of proximal point algorithms. More precisely, we study a new type of generalization of the EM procedure introduced in [Chretien and Hero (1998)] and called Kullback-proximal algorithms. The proximal framework allows us to prove new results concerning the cluster points. An essential contribution is a detailed analysis of the case where some cluster points lie on the boundary of the parameter space.

DOI : 10.1051/ps:2007041
Classification : 65C20, 65C60
Mots clés : maximum likelihood estimation (MLE), EM algorithm, proximal point algorithm, Karush-Kuhn-Tucker condition, mixture densities, competing risks models 
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     author = {Chr\'etien, St\'ephane and Hero, Alfred O.},
     title = {On {EM} algorithms and their proximal generalizations},
     journal = {ESAIM: Probability and Statistics},
     pages = {308--326},
     publisher = {EDP-Sciences},
     volume = {12},
     year = {2008},
     doi = {10.1051/ps:2007041},
     mrnumber = {2404033},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps:2007041/}
}
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Chrétien, Stéphane; Hero, Alfred O. On EM algorithms and their proximal generalizations. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 308-326. doi : 10.1051/ps:2007041. http://www.numdam.org/articles/10.1051/ps:2007041/

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