Functional (Statistics)

Definition

$T$ is called a functional if $T$ is a function of CDF or PDF

Let $X_1,X_2,\dots ,X_n$ be Random Sample from a cdf $F(x)$ and $T(F)$ be functional, then the empirical Distribution Function of $F$ at $x$ is ${\hat{F}}_n(x)=\frac{1}{n}\sum _{i=1}^{n}I(X_i\le x)$, and $T({\hat{F}}_n)$ is called an induced estimator of $T(F)$.