Cramer-Rao bound characterization of the EM-algorithm mean speed of convergence

Herzet, Cedric Ramon, Valery [UCL] Renaux, Alexandre Vandendorpe, Luc [UCL]

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.