Generalized Barankin-type lower bounds for misspecified models

Abstract

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.