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As is well known, the Cramér-Rao bound (or information inequality) sets a lower bound on the variance of estimators of a parameter. Consider the case when the parameter is a scalar, the estimator is ...

The Fisher information of a random variable $Y$ about a parameter $\theta$ upon which the probability of $Y$ depends is: $\mathcal{I}_Y(\theta)= -E\left[\left.\strut \frac{\partial^2}{\partial \theta^...