On the efficiency of maximum-likelihood estimators of misspecified models
M L Diong, Éric Chaumette, François Vincent · 2017
The key results on maximum-likelihood (ML) estimation of misspecified models have been introduced by statisticians (P.J. Huber, H. Akaike, H. White, Q. H. Vuong) resorting to a general probabilistic formalism somewhat difficult to rephrase into the formalism widespread in the signal processing literature. In particular, Vuong proposed two misspecified Cramer-Rao bounds (CRBs) to address, respectively, the situation where the true parametric probability model is known, or not known. In this communication, derivations of the existing results on the accuracy of ML estimation of misspecified models are outlined in an easily comprehensible manner. Simple alternative derivations of these two misspecified CRBs based on the seminal work of Barankin (which underlies all the lower bounds introduced in deterministic estimation) are provided. Since two distinct CRBs exist when the true parametric probability model is known, a quasi-efficiency denomination is introduced.