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 $L(F, \hat{F}) = \int (\hat{F}(t) - F(t))^2(F(t))^\alpha(1 - F(t))^b dW(t)$ 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.
Publié le : 1985-03-14
Classification:
Admissibility,
empirical distribution function,
i.i.d. sample,
weighted quadratic loss,
simple random sampling without replacement,
finite population,
multinomial distribution,
62C15,
62G30,
62D05
@article{1176346591,
author = {Cohen, Michael P. and Kuo, Lynn},
title = {The Admissibility of the Empirical Distribution Function},
journal = {Ann. Statist.},
volume = {13},
number = {1},
year = {1985},
pages = { 262-271},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346591}
}
Cohen, Michael P.; Kuo, Lynn. The Admissibility of the Empirical Distribution Function. Ann. Statist., Tome 13 (1985) no. 1, pp. 262-271. http://gdmltest.u-ga.fr/item/1176346591/