Hybrid lower bound on the MSE based on the Barankin and Weiss-Weinstein bounds

Abstract

This article investigates hybrid lower bounds in order to predict the estimators mean square error threshold effect. A tractable and computationally efficient form is derived. This form combines the Barankin and the Weiss-Weinstein bounds. This bound is applied to a frequency estimation problem for which a closed-form expression is provided. A comparison with results on the hybrid Barankin bound shows the superiority of this new bound to predict the mean square error threshold.

A Ziv-Zakaï type bound for hybrid parameter estimation

“…In the hybrid context, a bound including the Weiss-Weinstein bound for the random part has already been proposed [5]. The purpose of the present paper is to provide a hybrid bound including the ZivZakaï bound for the random part.…”

“…In order to fill this lack, other hybrid lower bounds have already been proposed, e.g. the Hybrid Barankin Bound (HBB) [4] or the Hybrid Barankin/WeissWeinstein bound (HBWWB) [5]. In each case, the key idea is to combine, in a tricky way, some lower bounds already known in the Bayesian and non-Bayesian framework.…”

“…In each case, the key idea is to combine, in a tricky way, some lower bounds already known in the Bayesian and non-Bayesian framework. So far this combination has been done by resorting to the covariance inequality principle which seems to be the cornerstone to establish such hybrid lower bounds [5] [6].…”

“…If the Weiss-Weinstein family is based on the covariance inequality principle, leading to a natural extension to the hybrid context [5], the Ziv-Zakaï family [7] is based on a binary hypothesis testing problem not a priori linked to the covariance inequality principle. A first consequence is the necessity to resort to simulation in order to compare the tightness of these two families.…”

A constrained hybrid Cramér-Rao bound for parameter estimation

“…This limitation can be overcome by resorting to other hybrid lower bounds, e.g. the Hybrid Barankin Bound (HBB) [4], the Hybrid Barankin/WeissWeinstein bound (HBWWB) [5] or the Hybrid Barankin/Ziv-Zakaï bound (HBZZB) [6]. Unfortunately, the computational cost of these hybrid "large-error" bounds is prohibitive in most applications when the number of unknown parameters increases.…”