Une version de type recuit simulé de l’algorithme EM. (A simulated annealing type EM algorithm). (French) Zbl 0693.62035

Celeux, Gilles; Diebolt, Jean

C. R. Acad. Sci., Paris, Sér. I 310, No. 3, 119-124 (1990).

Summary: The EM algorithm concerns maximum likelihood estimation for incomplete data. We present a simulated annealing type EM algorithm: SAEM. This algorithm is an adaptation of the stochastic EM algorithm (SEM) that we have previously developed [see Rev. Stat. Appl. 34, No.2, 35-52 (1986)]. Like SEM, SAEM overcomes most of the well-known limitations of EM. Moreover, SAEM performs better for small samples. Here, we focus on the mixture problem. We state a theorem which asserts that each SAEM sequence converges a.s. to a local maximizer of the likelihood function.

MSC:

62F99	Parametric inference
65C99	Probabilistic methods, stochastic differential equations

Keywords:

maximum likelihood estimation for incomplete data; simulated annealing type EM algorithm; SAEM; stochastic EM algorithm; SEM; mixture problem; local maximizer of the likelihood function