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Article Dans Une Revue IEEE Transactions on Signal Processing Année : 2008

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

Résumé

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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Dates et versions

inria-00444732 , version 1 (07-01-2010)

Identifiants

  • HAL Id : inria-00444732 , version 1

Citer

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, 2008, 56 (6), pp.2218-2228. ⟨inria-00444732⟩
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