A Generalized Ziv-Zakai Lower Bound on the Minimum Mean Squared Error

This paper presents the most general versions of the Ziv-Zakai family of lower bounds on the minimum mean squared error (MMSE) in estimation problems. The bounds are derived without any assumptions on the distribution of the parameter being estimated, making them applicable to discrete, continuous, and mixed distributions. The paper also analyzes the high-noise and low-noise asymptotics of the bounds, and provides insights on their tightness and comparison to other standard Bayesian MMSE lower bounds.