The efficiency of a statistic
is the degree to which the statistic is stable from sample to sample. That is, the less subject to sampling fluctuation
a statistic is, the more efficient it is. The efficiency of statistics is measured relative to the efficiency of other statistics and is therefore often called the relative efficiency. If statistic A has a smaller standard error
than statistic B, then statistic A is more efficient than statistic B.
The relative efficiency of two statistics may depend on the distribution
involved. For instance, the mean
is more efficient
than the median
but not for some extremely skewed
The efficiency of a statistic can also be thought of as the precision of the estimate: The more efficient the statistic, the more precise the statistic is as an estimator of the parameter.