A CramÉr-Rao Bound Characterization of the EM-Algorithm Mean Speed of Convergence

This paper deals with the mean speed of convergence of the expectation-maximization (EM) algorithm. We show that the asymptotic behavior (in terms of the number of observations) of the EM algorithm can be characterized as a function of the Cramer-Rao bounds (CRBs) associated to the so-called incompl...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2008-06, Vol.56 (6), p.2218-2228
Main Authors: Herzet, C., Ramon, V., Renaux, A., Vandendorpe, L.
Format: Article
Language:English
Subjects:
Applied sciences
Computer Science
Convergence
Convergence of numerical methods
Engineering Sciences
Exact sciences and technology
Genetic expression
Information, signal and communications theory
Iterative algorithms
Iterative methods
Laboratories
Maximum likelihood estimation
Miscellaneous
Phase estimation
Remote sensing
Robustness
Signal and Image Processing
Signal processing
State estimation
Telecommunications and information theory
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Summary:This paper deals with the mean speed of convergence of the expectation-maximization (EM) algorithm. We show that the asymptotic behavior (in terms of the number of observations) of the EM algorithm can be characterized as a function of the Cramer-Rao bounds (CRBs) associated to the so-called incomplete and complete data sets defined within the EM-algorithm framework. We particularize our result to the case of a complete data set defined as the concatenation of the observation vector and a vector of nuisance parameters, independent of the parameter of interest. In this particular case, we show that the CRB associated to the complete data set is nothing but the well-known modified CRB. Finally, we show by simulation that the proposed expression enables to properly characterize the EM-algorithm mean speed of convergence from the CRB behavior when the size of the observation set is large enough.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2008.917024