Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound
Foundations and Trends in Signal Processing
Uniformly Improving the CramÉr-Rao Bound and Maximum-Likelihood Estimation
IEEE Transactions on Signal Processing
MSE Bounds With Affine Bias Dominating the CramÉr–Rao Bound
IEEE Transactions on Signal Processing - Part II
Minimum variance in biased estimation: bounds and asymptotically optimal estimators
IEEE Transactions on Signal Processing
Exploring estimator bias-variance tradeoffs using the uniform CRbound
IEEE Transactions on Signal Processing
Extended Ziv-Zakai lower bound for vector parameter estimation
IEEE Transactions on Information Theory
A Comment on the Weiss–Weinstein Bound for Constrained Parameter Sets
IEEE Transactions on Information Theory
IEEE Transactions on Image Processing
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A lower bound on the minimum mean-squared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a well-known connection to the deterministic estimation setting. Using the prior distribution, the bias function which minimizes the Cramér-Rao bound can be determined, resulting in a lower bound on the Bayesian MSE. The bound is developed for the general case of a vector parameter with an arbitrary probability distribution, and is shown to be asymptotically tight in both the high and low signal-to-noise ratio (SNR) regimes. A numerical study demonstrates several cases in which the proposed technique is both simpler to compute and tighter than alternative methods.