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首页> 外文期刊>IEEE Transactions on Information Theory >A Class of Weiss–Weinstein Bounds and Its Relationship With the Bobrovsky–Mayer-Wolf–Zakaï Bounds
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A Class of Weiss–Weinstein Bounds and Its Relationship With the Bobrovsky–Mayer-Wolf–Zakaï Bounds

机译：一类Weiss–Weinstein界及其与Bobrovsky–Mayer-Wolf–Zakaï界的关系

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摘要

A fairly general class of Bayesian “large-error” lower bounds of the Weiss-Weinstein family, essentially free from regularity conditions on the probability density functions support, and for which a limiting form yields a generalized Bayesian Cramér-Rao bound (BCRB), is introduced. In a large number of cases, the generalized BCRB appears to be the Bobrovsky-Mayer-Wolf-Zakai bound (BMZB). Interestingly enough, a regularized form of the Bobrovsky-Zakai bound (BZB), applicable when the support of the prior is a constrained parameter set, is obtained. Modified Weiss-Weinstein bound and BZB which limiting form is the BMZB are proposed, in expectation of an increased tightness in the threshold region. Some of the proposed results are exemplified with a reference problem in signal processing: the Gaussian observation model with parameterized mean and uniform prior.
机译：Weiss-Weinstein族的一个相当通用的贝叶斯“大错误”下界，基本上没有概率密度函数支持的正则条件，并且对其的限制形式产生了广义贝叶斯Cramér-Rao界（BCRB），介绍。在许多情况下，广义BCRB似乎是Bobrovsky-Mayer-Wolf-Zakai界（BMZB）。有趣的是，获得了Bobrovsky-Zakai边界（BZB）的正则化形式，适用于先验的支持是受约束的参数集的情况。提出了改进的Weiss-Weinstein界和BZB（其限制形式为BMZB），以期在阈值区域中提高密封性。一些提出的结果以信号处理中的参考问题为例：具有参数化均值和均匀先验的高斯观测模型。

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