Consider the problem of estimating the ordered means $\mu_1 \leq \mu_2 \leq \cdots \leq \mu_k$ of independent normal random variables, $Y_1, Y_2, \cdots, Y_k$. It is shown that the absolute error of each component $\hat{\mu}_i$ of the isotonic regression estimator is stochastically smaller than that of the usual estimator $Y_i$. Thus $\hat{\mu}_i$ is superior to $Y_i$ under any nonconstant loss which is a nondecreasing function of absolute error.
Publié le : 1989-06-14
Classification:
Isotonic regression,
loss function,
maximum likelihood,
order restriction,
stochastic ordering,
62F10,
62E99,
62C99,
60E15
@article{1176347153,
author = {Kelly, Robert E.},
title = {Stochastic Reduction of Loss in Estimating Normal Means by Isotonic Regression},
journal = {Ann. Statist.},
volume = {17},
number = {1},
year = {1989},
pages = { 937-940},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347153}
}
Kelly, Robert E. Stochastic Reduction of Loss in Estimating Normal Means by Isotonic Regression. Ann. Statist., Tome 17 (1989) no. 1, pp. 937-940. http://gdmltest.u-ga.fr/item/1176347153/