Generalized Barankin-type lower bounds for misspecified models
M L Diong, Éric Chaumette, François Vincent · 2017
When the assumed probability distribution of the observations differs from the true distribution, the model is said to be misspecified. The key results on maximum-likelihood estimation of misspecified models have been introduced in the limit of large sample support and depend on a parameters vector solution of a computationally expensive non-linear optimization problem. As a possible strategy to circumvent these limitations, we extend the approach lately proposed by Fritsche et al [1]. It is shown that the lower bound derived in [1] is a representative of a family of lower bounds deriving from a misspecified unbiasedness constraint leading to generalized Barankin-type lower bounds. For future use, we derive the standard representative of the “Small Errors” and “Large Errors” bounds, namely the generalized CRB and the generalized McAulay-Seidman bound.