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For an unbiased estimator, efficiency indicates how much its precision is lower than the theoretical limit of precision provided by the Cramer-Rao inequality. A measure of efficiency is the ratio of the theoretically minimal variance to the actual variance of the estimator. This measure falls between 0 and 1. An estimator with efficiency 1.0 is said to be an “efficient estimator”.

The efficiency of a given estimator depends on the population. For example, for a normally distributed population, the sample mean is an efficient estimator of the population mean. But the sample mean is usually not an efficient estimator of the mean of a non-normal population.

The efficiency of an estimator should not be confused with the relative efficiency (of statistical tests).

See also: Asymptotic efficiency

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