Definition:Efficiency (Statistics)

Definition

Let $T_0$ and $T_1$ both be statistics used as estimators.

Efficiency is a comparison of the variances of $T_0$ and $T_1$.

Thus $T_0$ is of higher efficiency than $T_1$ if and only if $T_0$ has a smaller variance than $T_1$.

Also see

• Definition:Relative Efficiency
• Definition:Asymptotic Relative Efficiency

• Results about efficiency in the context of statistics can be found here.

Historical Note

The concept of efficiency in the context of statistics was pioneered by Ronald Aylmer Fisher in $1921$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): efficiency: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): efficiency: 1.