The Admissibility of the Empirical Distribution Function
The Admissibility of the Empirical Distribution Function
Consider the problem of estimating an unknown distribution function $F$ from the class of all distribution functions given a random sample of size $n$ from $F$. It is proved that the empirical distribution function is admissible for the loss functions $L(F, \hat{F}) = \int (\hat{F}(t) - F(t))^2(F(t))^\alpha(1 - F(t))^b dW(t)$ …