Definition:Relative Efficiency

Definition

Let $T_1$ and $T_2$ be estimators of a parameter $\theta$.

Let $n_1$ and $n_2$ respectively be the sample sizes needed to give $T_1$ and $T_2$ the same variance.

The relative efficiency of $T_1$ with respect to $T_2$ is defined as $\dfrac {n_2} {n_1}$.

Examples

Arbitrary Example

Let $n_1 = 10$ and $n_2 = 20$.

Then the relative efficiency of $T_1$ with respect to $T_2$ is $\dfrac {20} {10} = 2$.

Thus $T_1$ is twice as efficient as $T_2$.

Also see

• Definition:Asymptotic Relative Efficiency

• Results about relative efficiency can be found here.

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.