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The Cramér–Rao bound is stated in this section for several increasingly general cases, beginning with the case in which the parameter is a scalar and its estimator is unbiased.
Equivalently, the estimator achieves equality in the Cramér–Rao inequality for all θ. The Cramér–Rao lower bound is a lower bound of the variance of an unbiased estimator, representing the "best" an unbiased estimator can be. An efficient estimator is also the minimum variance unbiased estimator (MVUE). This is because an efficient ...
The quantum Cramér–Rao bound is the quantum analogue of the classical Cramér–Rao bound. It bounds the achievable precision in parameter estimation with a quantum system: It bounds the achievable precision in parameter estimation with a quantum system:
For the Cramér–Rao inequality and the Rao–Blackwell theorem see the relevant entries on Earliest Known Uses of Some of the Words of Mathematics; For Rao contribution to information geometry Cramer-Rao Lower Bound and Information Geometry; Photograph of Rao with Harald Cramér in 1978 C. R. Rao from the PORTRAITS OF STATISTICIANS
Download as PDF; Printable version ... In information theory and statistics, Kullback's inequality is a lower bound on the Kullback ... The Cramér–Rao bound is a ...
That is, there is a decomposition for which the second inequality is saturated, which is the same as stating that the quantum Fisher information is the convex roof of the variance over four, discussed above. There is also a decomposition for which the first inequality is saturated, which means that the variance is its own concave roof [14]
that “they” should manage our rights, the way we hire a professional to do our taxes; “they” should run the government, create policy, worry about whether democracy is up and running.
A great many important inequalities in information theory are actually lower bounds for the Kullback–Leibler divergence.Even the Shannon-type inequalities can be considered part of this category, since the interaction information can be expressed as the Kullback–Leibler divergence of the joint distribution with respect to the product of the marginals, and thus these inequalities can be ...