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

Cédric Herzet; Valéry Ramon; Alexandre Renaux; Luc Vandendorpe

inria-00444732, version 1

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

Cédric Herzet ()^a^, 1, Valéry Ramon ², Alexandre Renaux ()^b^, 3, Luc Vandendorpe^c^, 2

IEEE Transactions on Signal Processing 56, 6 (2008) 2218-2228

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.

a – INRIA
b – Université de Paris-Sud Orsay
c – Université Catholique de Louvain
1: TEMICS (INRIA - IRISA)
CNRS : UMR6074 – INRIA – Université de Rennes 1
2: Laboratoire de Télédétection et Télécommunications (TELE)
Université Catholique de Louvain (UCL) - Belgique
3: Laboratoire des signaux et systèmes (L2S)
UMR8506 CNRS – SUPELEC – Université Paris XI - Paris Sud

inria-00444732, version 1
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From: Alexandre Renaux <>
Submitted on: Thursday, 7 January 2010 11:32:22
Updated on: Monday, 11 January 2010 12:52:59

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