Asymptotic properties of posterior distributions derived from misspecified models
Christophe Abraham, Benoı̂t Cadre · Comptes Rendus Mathématique · 2002
We investigate the asymptotic properties of posterior distributions when the model is misspecified, i.e. it is contemplated that the observations x 1 ,…, x n might be drawn from a density in a family { h σ , σ ∈ Θ } where Θ ⊂ ℝ d , while the actual distribution of the observations may not correspond to any of the densities h σ . A concentration property around a fixed value of the parameter is obtained as well as concentration properties around the maximum likelihood estimate.