When a unique $M$-estimate exists, its density is obtained as a
corollary to a more general theorem which asserts that under mild conditions
the intensity function of the point process of solutions of the estimating
equations exists and is given by the density of the estimating function
standardized by multiplying it by the inverse of its derivative. We apply the
results to give a result for Huber’s proposal 2 applied to regression
and scale estimates. We also give a saddlepoint approximation for the density
and use this to give approximations for tail areas for smooth functions of the
$M$-estimates.
Publié le : 2000-02-14
Classification:
Intensity,
$M$-estimator,
point process,
62E17,
62F11,
60G55
@article{1016120373,
author = {Almudevar, Anthony and Field, Chris and Robinson, John},
title = {The density of multivariate $M$-estimates},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 275-297},
language = {en},
url = {http://dml.mathdoc.fr/item/1016120373}
}
Almudevar, Anthony; Field, Chris; Robinson, John. The density of multivariate $M$-estimates. Ann. Statist., Tome 28 (2000) no. 3, pp. 275-297. http://gdmltest.u-ga.fr/item/1016120373/