Improved Ziv-Zakai lower bound for vector parameter estimation

Abstract

The Ziv-Zakai (1969) bounds on the mean square error (MSE) in parameter estimation are some of the tightest available bounds. These bounds relate the MSE in the estimation problem to the probability of error in a binary hypothesis testing problem. The original Bayesian version derived by Ziv and Zakai, and improvements by Chazan, Zakai and Ziv (1975) and Bellini and Tartara (1974) are applicable to scalar random variables with uniform prior distributions. This bound was extended by Bell, Ephraim, Steinberg and Van Trees (see Proceedings of 1994 International Symposium on Information Theory, Trondheim, Norway, June 1994) to vectors of random variables with arbitrary prior distributions. The goal of this paper is to present an improvement to the vector version of Bell et. al., explore some properties of the bounds, and present further generalizations.