Les modèles non linéaires à effets mixtes - Isped

Estimation of the Fisher Information matrix
An estimate of the asymptotic covariance matrix of ̂θ g is the inverse of
the observed Fisher Information matrix :
−∂ 2 θ log g(y; ̂θ g )
Louis’s missing information principle (1982)
∂θ 2 log g(y; θ) = E y;θ[∂θ 2 log f(y, φ; θ)] + Cov y;θ[∂ θ log f(y, φ; θ)]
where
Cov y;θ [∂ θ log f(y, φ; θ)] = E y;θ [ ( ∂ θ log f(y, φ; θ) )( ∂ θ log f(y, φ; θ) ) ′ ]
− E y;θ [∂ θ log f(y, φ; θ)]E y;θ [∂ θ log f(y, φ; θ)] ′
and
∂ θ log g(y; θ) = E y;θ [∂ θ log f(y, φ; θ)]
Sminaire ”Statistique et Sant Publique”, Bordeaux - 8 novembre 2005, p.32