We study nonparametric estimation of convexregression and density
functions by methods of least squares (in the regression and density cases) and
maximum likelihood (in the density estimation case).We provide
characterizations of these estimators, prove that they are consistent and
establish their asymptotic distributions at a fixed point of positive curvature
of the functions estimated. The asymptotic distribution theory relies on the
existence of an “invelope function” for integrated two-sided
Brownian motion $+t^4$ which is established in a companion paper by Groeneboom,
Jongbloed and Wellner.
Publié le : 2001-12-14
Classification:
Convex,
dinsity estimation,
regression function,
maximum likelihood,
least squares,
integrated Brownian motion,
62G05,
62G07,
62G08,
62E20
@article{1015345958,
author = {Groeneboom, Piet and Jongbloed, Geurt and Wellner, Jon A.},
title = {Estimation of a Convex Function: Characterizations and
Asymptotic Theory},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 1653-1698},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345958}
}
Groeneboom, Piet; Jongbloed, Geurt; Wellner, Jon A. Estimation of a Convex Function: Characterizations and
Asymptotic Theory. Ann. Statist., Tome 29 (2001) no. 2, pp. 1653-1698. http://gdmltest.u-ga.fr/item/1015345958/