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 \[ L(F,\hat F)=\int (\hat F(t)-F(t))^ 2(F(t))^ a(1-F(t))^ bdW(t) \] for any \(a<1\) and \(b<1\) and finite measure W. Related results for simultaneous estimation of distribution functions and for finite population sampling are also given.
simple random sampling without replacement
multivariate hypergeometric distribution
scientific article; zbMATH DE number 3919532