Cramér-Rao revisited

Lenstra, Andries

doi:10.3150/bj/1116340294

Cited by 7 publications

(4 citation statements)

References 8 publications

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“…The uncertainties related to the noise can be calculated by estimating the CRBs from the Fisher information matrix [7], [8], [9], [10], [11]. Using Eq.…”

Section: B Error Estimation On the Background Data-pointsmentioning

confidence: 99%

Semi-Parametric Estimation in Magnetic Resonance Spectroscopy: Automation of the Disentanglement Procedure

Rabeson

Ratiney

Ormondt

et al. 2007

2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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Semi-parametric disentanglement of parametric parts from non-parametric parts of a signal is a universal problem. This study concerns estimation of metabolite concentrations from in vivo Magnetic Resonance Spectroscopy (MRS) signals. Due to in vivo conditions, so-called macro-molecules contribute non-parametric components to the signals. Disentanglement is achieved by exploiting prior knowledge about the parametric and non-parametric parts directly in the measurement domain. Moreover, Cramér-Rao bounds on the non-parametric part are derived. These expressions are used to automate the disentanglement procedure.

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“…The uncertainties related to the noise can be calculated by estimating the CRBs from the Fisher information matrix [7], [8], [9], [10], [11]. Using Eq.…”

Section: B Error Estimation On the Background Data-pointsmentioning

confidence: 99%

Semi-Parametric Estimation in Magnetic Resonance Spectroscopy: Automation of the Disentanglement Procedure

Rabeson

Ratiney

Ormondt

et al. 2007

2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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“…A careful version of (1.5) under very weak assumptions was given (for Θ = R) by Lenstra [6]. Some applications and generalisations have been considered by Bobrovsky et al [7] and by Brown and Gajek [8].…”

Section: Introductionmentioning

confidence: 96%

A van Trees inequality for estimators on manifolds

Jupp

2010

Journal of Multivariate Analysis

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a b s t r a c t 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 Gill and Levit (1995) [R.D. Gill, B.Y. Levit, Applications of the van Trees inequality: a Bayesian Cramér-Rao bound, Bernoulli 1 (1995) 59-79]. In addition, the intrinsic Cramér-Rao inequality of Hendriks (1991) [H. Hendriks, A Cramér-Rao type lower bound for estimators with values in a manifold, J. Multivariate Anal. 38 (1991) 245-261] 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.

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“…Нижнюю границу средне-квадратической ошибки в случае регулярного параметрического семейства распределений устанавливает знаменитое неравенство Фреше-Рао-Крамера; нижние границы средне-квадратической ошибки известны также для параметрических семейств с определенными нерегулярностями [14], [21].…”

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“…Неравенства (12)- (14) показывают, что естественной нормирующей последовательностью для αn/α F − 1 является…”

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