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A van Trees inequality for estimators on manifolds. (English) Zbl 1352.62043

Summary: Van Trees’ Bayesian version of the Cramér-Rao inequality is generalised here to the context of smooth loss functions on manifolds and estimation of parameters of interest. This extends the multivariate van Trees inequality of R. D. Gill and B. Y. Levit [Bernoulli 1, No. 1–2, 59–79 (1995; Zbl 0830.62035)]. In addition, the intrinsic Cramér-Rao inequality of H. Hendricks [J. Multivariate Anal. 38, No. 2, 245–261 (1991; Zbl 0753.62032)] is extended to cover estimators which may be biased. The quantities used in the new inequalities are described in differential-geometric terms. Some examples are given.

MSC:

62F10 Point estimation
62F15 Bayesian inference
62B10 Statistical aspects of information-theoretic topics
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References:

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