Les modèles non linéaires à effets mixtes - Isped

Convergence of the algorithm
(Kuhn and Lavielle)
Theorem
- Assume that the regularity conditions required for the convergence
of EM are satisfied
- Assume that assumptions C1-C3 hold
- Assume that for any θ ∈ Θ, the sequence (Q k (θ)) k≥0 takes its
values in a compact subset of S.
Then, w.p. 1, lim k→+∞ d(θ k , L) = 0 where d(x, A) denotes the distance
of x to the closed subset A and L = {θ ∈ Θ, ∂ θ g(y; θ) = 0} is the set of
stationary points of g.
(Some weak hypothesis ensure the convergence to a (local) maximum
of the likelihood)
Sminaire ”Statistique et Sant Publique”, Bordeaux - 8 novembre 2005, p.31