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

Abstract : 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 Cramér-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.
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IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2008, 56 (6), pp.2218-2228
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Dernière modification le : mercredi 11 avril 2018 - 01:57:39
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  • HAL Id : inria-00444732, version 1

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Cédric Herzet, Valéry Ramon, Alexandre Renaux, Luc Vandendorpe. A Cramer-Rao Bound Characterization of the EM-Algorithm Mean Speed of Convergence. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2008, 56 (6), pp.2218-2228. 〈inria-00444732〉

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