Tractable forms of some deterministic MSE lower bounds for biased estimation

The aim of this paper is to investigate some deterministic lower bounds for biased estimation. Namely, the Cramer-Rao bound (CRB) and the Chapman-Robbins bound (ChRB) are addressed. First, a modified version of the ChRB accounting for estimation bias is derived and shown to be tighter than the CRB accounting for bias. Then, an approximation of the estimation bias is proposed and used to provide tractable forms of the studied bounds. Finally, the obtained bounds relevance is assessed in the frame of Maximum Likelihood (ML) frequency estimation.