基于最优偏差函数的贝叶斯MSE的一个下界
A Lower Bound on the Bayesian MSE Based on the Optimal Bias Function
摘要：
本文提出了贝叶斯估计问题中最小均方误差（MSE）的一个下界。该界限利用了与确定性估计设置的众所周知的连接。使用先验分布，可以确定使Cramer-Rao界最小化的偏差函数，从而得到贝叶斯MSE的下界。边界开发的一般情况下，具有任意概率分布的矢量参数，并被证明是渐近紧的高和低的信号-噪声比制度。数值研究表明，在几种情况下，所提出的技术是更简单的计算和更紧密的替代方法。
英文摘要：
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 Cramer-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 regimes. A numerical study demonstrates several cases in which the proposed technique is both simpler to compute and tighter than alternative methods.
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