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Cramer – Rao Inequality

Cramer – Rao Inequality:

Every unbiased estimator has a variance greater than or equal to a lower bound called the Cramer – Rao lower bound. If the variance of an unbiased estimator achieves the Cramer – Rao lower bound, then that estimator is a minimum variance unbiased estimator, or, simply, efficient estimator (see Efficiency).

To use the Cramer – Rao inequality in a particular situation you have to know the expression for the likelihood function and the likelihood function should satisfy some regularity conditions (otherwise the Cramer – Rao inequality is not applicable).

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