Almost sure convergence of Titterington's recursive estimator for mixture models

Titterington proposed a recursive parameter estimation algorithm for finite mixture models. However, due to the well known problem of singularities and multiple maximum, minimum and saddle points that are possible on the likelihood surfaces, convergence analysis has seldom been made in the past year...

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Bibliographic Details
Published inStatistics & probability letters Vol. 76; no. 18; pp. 2001 - 2006
Main Authors Wang, Shaojun, Zhao, Yunxin
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.12.2006
Elsevier
SeriesStatistics & Probability Letters
Subjects
Almost sure convergence
Exact sciences and technology
Incomplete data
Mathematics
Mixture model
Probability and statistics
Recursive estimation
Recursive estimation Incomplete data Mixture model Regular exponential family Almost sure convergence Stochastic approximation
Regular exponential family
Sciences and techniques of general use
Sequential methods
Statistics
Stochastic approximation
Mixture model
Incomplete data
Stochastic approximation
Almost sure convergence
Regular exponential family
Recursive estimation
Singularity
Parameter estimation
Probability theory
Surface analysis
Recursive algorithm
Saddle point
Statistical method
Mixed model
Exponential family
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Summary:Titterington proposed a recursive parameter estimation algorithm for finite mixture models. However, due to the well known problem of singularities and multiple maximum, minimum and saddle points that are possible on the likelihood surfaces, convergence analysis has seldom been made in the past years. In this paper, under mild conditions, we show the global convergence of Titterington's recursive estimator and its MAP variant for mixture models of full regular exponential family.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2006.05.017