Let $X_1,\dots,X_n$ be identically but not necessary independent distributed with distribution function $F$. I'd like to estimate $F$ efficiently.
In case, $X_1,\dots,X_n$ are i.i.d., we can estimate $F$ by $\hat F_n(x)=\frac1n\sum_{i=1}^n1_{\{X_i\le x\}}$.
$\hat F_n$ is efficient for estimating $F$ since we can verify easily that $var(\hat F_n)$ is the smallest variance among all unbiased estimators.
However, since in my problem, I don't have the i.i.d. condition, so what should I do? Any help will be appreciated.
