Convergence of a stochastic approximation version of the EMalgorithmMarc Lavielle

SUMMARY The Expectation-Maximization (EM) algorithm is a powerful computational technique for locating maxima of functions. It is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data models. In certain situations however, this method is not applicable because the expectation step cannot be performed in closed{form. To deal with these problems, a novel method is introduced, the Stochastic Approximation EM (SAEM), which consists in replacing the expectation step of the EM algorithm by one iteration of a stochastic approximation procedure. The convergence of the SAEM algorithm is established under conditions that are applicable to many practical situations. Moreover it is proved that, under mild additional conditions, the attractive stationary points of the SAEM algorithm correspond to the local maxima of the function. Simple illustrative examples of applications of the SAEM algorithm are presented to support our ndings.

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