Asymptotically Optimal (Efficient)

Table of contents

1. Asymptotic Relative Efficiency (ARE)

---

Asymptotic Relative Efficiency (ARE)

When we have two estimators $T_n$ and $U_n$ for the same parameter, we can compare their variances to see which one is more efficient.

Obviously, the smaller the variance, the better the estimator.

The asymptotic relative efficiency (ARE) of $U_n$ to $T_n$ is defined as:

$$ \text{ARE}(U_n, T_n) = \frac{\Var(T_n)}{\Var(U_n)} $$

If $\text{ARE}(U_n, T_n) \leq 1$, then $T_n$ is more efficient than $U_n$.