Title :
Improved Ziv-Zakai lower bound for vector parameter estimation
Author :
Bell, Kristine L. ; Steinberg, Yossef ; Ephraim, Yariv ; Van Trees, Harry L.
Author_Institution :
Dept. of Electr. & Comput. Eng., George Mason Univ., Fairfax, VA, USA
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
Keywords :
error analysis; parameter estimation; probability; signal processing; statistical analysis; vectors; Ziv-Zakai lower bound; binary hypothesis testing; error probability; mean square error; scalar random variables; uniform prior distributions; vector parameter estimation; vector random variables; Bayesian methods; Density functional theory; Detectors; Estimation error; Euclidean distance; Parameter estimation; Probability density function; Random variables; Testing; Vectors;
Conference_Titel :
Information Theory and Statistics, 1994. Proceedings., 1994 IEEE-IMS Workshop on
Conference_Location :
Alexandria, VA
Print_ISBN :
0-7803-2761-6
DOI :
10.1109/WITS.1994.513904
