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Cramer Rao Inequality, Cauchy-Binet Representation and Structural Optimization of Fluorescence Unmixing Experiment

2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI), 2020
A predictive theoretical model based on Cramer-Rao bound for the uncertainty in fluorescent protein mixture composition detection has been developed. A physically based representation of the experimental efficiency through the Cauchy-Binet identity is presented.
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Zipf's law results from the scaling invariance of the Cramer–Rao inequality

Handbook of Statistics, 2021
A Plastino, Alberto Hernando De Castro
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THE CRAMÉR‐RAO INEQUALITY

Australian Journal of Statistics, 1978
SummaryThe essential significance of the Cram‐Rao inequality is investigated. This inequality states a relation between the rate of change of a mean value and a rate of change of the probability measure. Simple, general regularity conditions are obtained.
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On an analogue of Cramér-Rao's inequality

Scandinavian Actuarial Journal, 1958
Abstract Rao [1] and simultaneously Cramer [2, 3] have shown that if f (x, θ) is the probability density function of a distribution involving an unknown parameter θ and distributed over the range α ⩽ x ⩽ b, where a and b are independent of θ, and if x 1 x 2 ... x n is a random sample of n independent observations from this distribution, the variance of
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A Refinement of the Cramér-Rao Inequality

Theory of Probability & Its Applications, 1961
This paper deals with the strengthening of the Cramer-Rao information inequality when simultaneous estimates do not exist.
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Another Look at the Cramér-Rao Inequality

The American Statistician, 2001
The Cramer–Rao inequality is obtained as a direct corollary of (i) monotonicity of the Fisher information and (ii) a lower bound for the information in linear models. The proof connects the fundamental inequality with linear models and has methodological advantages over the standard proof.
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