Asymptotic Relative Efficiency

A measure of the performance of two statistical procedures, either tests or estimators, as sample size ${\lim }_{n\to \infty }$. Defined as the limit of the ratio $\frac{n_2}{n_1}$ needed for achieving statistical power/reciprocal ratio of their asymptotic variances.

Formally,

For two estimators $\widehat{{\theta }_1}$ and $\widehat{{\theta }_2}$ along with asymptotic variances ${\sigma }_1^2$ and ${\sigma }_2^2$, ARE is typically defined as $\frac{{\sigma }_2^2}{{\sigma }_1^2}$