A class of Weiss-Weinstein bounds and its relationship with the Bobrovsky-Mayer-Wolf-Zakai bounds

Abstract : 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.
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Eric Chaumette, Alexandre Renaux, Mohammed Nabil El Korso. A class of Weiss-Weinstein bounds and its relationship with the Bobrovsky-Mayer-Wolf-Zakai bounds. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2017, 63 (4), pp.2226-2240. ⟨10.1109/TIT.2017.2671883⟩. ⟨hal-01525497⟩

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