Efficiency (statistics)

In statistics, efficiency is a measure of quality of an estimator, of an experimental design,^[1] or of a hypothesis testing procedure.^[2] Essentially, a more efficient estimator needs fewer input data or observations than a less efficient one to achieve the Cramér–Rao bound. An efficient estimator is characterized by having the smallest possible variance, indicating that there is a small deviance between the estimated value and the "true" value in the L2 norm sense. ^[1]

The relative efficiency of two procedures is the ratio of their efficiencies, although often this concept is used where the comparison is made between a given procedure and a notional "best possible" procedure. The efficiencies and the relative efficiency of two procedures theoretically depend on the sample size available for the given procedure, but it is often possible to use the asymptotic relative efficiency (defined as the limit of the relative efficiencies as the sample size grows) as the principal comparison measure.