For a version of the interval censoring model, case 2, in which
the observation intervals are allowed to be arbitrarily small, we consider
estimation of functionals that are differentiable along Hellinger
differentiable paths. The asymptotic information lower bound for such
functionals can be represented as the squared $L_{2}$-norm of the canonical
gradient in the observation space. This canonical gradient has an implicit
expression as a solution of an integral equation that does not belong to one of
the standard types. We study an extended version of the integral equation that
can also be used for discrete distribution functions like the nonparametric
maximum likelihood estimator (NPMLE) , and derive the asymptotic normality and
efficiency of the NPMLE from properties of the solutions of the integral
equations.
Publié le : 1999-04-14
Classification:
Nonparametric maximum likelihood,
empirical processes,
asymptotic distributions,
asymptotic efficiency,
integral equations.,
60F17,
62E20,
62G05,
62G20,
45A05
@article{1018031211,
author = {Geskus, Ronald and Groeneboom, Piet},
title = {Asymptotically optimal estimation of smooth functionals for
interval censoring, case $2$},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 627-674},
language = {en},
url = {http://dml.mathdoc.fr/item/1018031211}
}
Geskus, Ronald; Groeneboom, Piet. Asymptotically optimal estimation of smooth functionals for
interval censoring, case $2$. Ann. Statist., Tome 27 (1999) no. 4, pp. 627-674. http://gdmltest.u-ga.fr/item/1018031211/