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

fYear

1994

fDate

27-29 Oct 1994

Firstpage

75

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory and Statistics, 1994. Proceedings., 1994 IEEE-IMS Workshop on

Conference_Location

Alexandria, VA

Print_ISBN

0-7803-2761-6

Type

conf

DOI

10.1109/WITS.1994.513904

Filename

513904