We show that nonparametric regression is asymptotically equivalent, in Le Cam’s sense, to a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework, based on approximation spaces, which allows asymptotic equivalence to be achieved, even in the cases of multivariate and random design.
Publié le : 2008-08-15
Classification:
Le Cam deficiency,
equivalence of experiments,
approximation space,
interpolation,
Gaussian white noise,
62G08,
62G20,
62B15
@article{1216237305,
author = {Rei\ss , Markus},
title = {Asymptotic equivalence for nonparametric regression with multivariate and random design},
journal = {Ann. Statist.},
volume = {36},
number = {1},
year = {2008},
pages = { 1957-1982},
language = {en},
url = {http://dml.mathdoc.fr/item/1216237305}
}
Reiß, Markus. Asymptotic equivalence for nonparametric regression with multivariate and random design. Ann. Statist., Tome 36 (2008) no. 1, pp. 1957-1982. http://gdmltest.u-ga.fr/item/1216237305/