We discuss in this paper asymptotics of locally optimal solutions
of maximum likelihood and,more generally, $M$-estimation procedures in cases
where the true value of the parameter vector lies on the boundary of the
parameter set $S$.We give a counterexample showing that regularity of $S$ in
the sense of Clarke is not sufficient for asymptotic equivalence of
$\sqrt{n}$-consistent locally optimal $M$-estimators.We argue further that
stronger properties, such as so-called near convexity or prox-regularity of $S$
are required in order to ensure that any two $\sqrt{n}$-consistent locally
optimal $M$-estimators have the same asymptotics.
Publié le : 2000-05-14
Classification:
Maximum likelihood,
contrained $M$-estimation,
asymptotic distribution,
tangent cones,
Clarke regularity,
prox-regularity,
metric projection,
62F12
@article{1015952006,
author = {Shapiro, Alexander},
title = {On the asymptotics of constrained local $M$-estimators},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 948-960},
language = {en},
url = {http://dml.mathdoc.fr/item/1015952006}
}
Shapiro, Alexander. On the asymptotics of constrained local $M$-estimators. Ann. Statist., Tome 28 (2000) no. 3, pp. 948-960. http://gdmltest.u-ga.fr/item/1015952006/