We identify the asymptotic behavior of the estimators proposed by
Rojo and Samaniego and Mukerjee of a distribution $F$ assumed to be uniformly
stochastically smaller than a known baseline distribution $G$.We show that
these estimators are $\sqrt{n}$-convergent to a limit distribution with mean
squared error smaller than or equal to the mean squared error of the empirical
survival function. By examining the mean squared error of the limit
distribution, we are able to identify the optimal estimator within
Mukerjee’s class under a variety of different assumptions on $F$ and
$G$. Similar theoretical results are developed for the two-sample problem
where$F$ and $G$ are both unknown. The asymptotic distribution theory is
applied to obtain confidence bands for the survival function $\bar{F}$ based on
published data from an accelerated life testing experiment.
@article{1016120367,
author = {Arcones, Miguel A. and Samaniego, Francisco J.},
title = {On the asymptotic distribution theory of a class of consistent
estimators of a distribution satisfying a uniform stochastic ordering
constraint},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 116-150},
language = {en},
url = {http://dml.mathdoc.fr/item/1016120367}
}
Arcones, Miguel A.; Samaniego, Francisco J. On the asymptotic distribution theory of a class of consistent
estimators of a distribution satisfying a uniform stochastic ordering
constraint. Ann. Statist., Tome 28 (2000) no. 3, pp. 116-150. http://gdmltest.u-ga.fr/item/1016120367/