High-Noise Asymptotics of the Ziv-Zakai Bound

The Ziv-Zakai bound is a well-known lower bound on the minimum mean squared error. This article analyzes the performance of this bound in the practically relevant high-noise regime for a broad family of observation models. The goal is to understand whether this bound is tight, and in which scenarios...

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Bibliographic Details
Published inIEEE signal processing letters Vol. 29; pp. 1933 - 1937
Main Authors Dytso, Alex, Cardone, Martina, Zieder, Ian
Format Journal Article
LanguageEnglish
Published New York IEEE 2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Bayes methods
Bayesian risk
Cramér-Rao bound
Error analysis
Estimation
Lower bounds
MMSE
Noise level
Noise measurement
Probability density function
Random variables
Upper bound
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Summary:The Ziv-Zakai bound is a well-known lower bound on the minimum mean squared error. This article analyzes the performance of this bound in the practically relevant high-noise regime for a broad family of observation models. The goal is to understand whether this bound is tight, and in which scenarios it should be used. It is shown that, while the Ziv-Zakai bound is tight for a certain class of symmetric distributions, in general, it is not tight in the high-noise regime.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2022.3203908