A TIGHTER BAYESIAN CRAMER-RAO BOUND

It has been shown lately that any "standard" Bayesian lower bound (BLB) on the mean squared error (MSE) of the Weiss-Weinstein family (WWF) admits a "tighter" form which upper bounds the "standard" form. Applied to the Bayesian Cramer-Rao bound (BCRB), this result suggests to redefine the concept of efficient estimator relatively to the tighter form of the BCRB, an update supported by a noteworthy example. This paper lays the foundation to revisit some Bayesian estimation problems where the BCRB is not tight in the asymptotic region.
Funding Agencies|DGA/MRIS [2018.60.0072.00.470.75.01]; Excellence Center at Linkoping and Lund in Information Technology (ELLIIT)