We derive the asymptotic distribution of a new backfitting
procedure for estimating the closest additive approximation to a nonparametric
regression function. The procedure employs a recent projection interpretation
of popular kernel estimators provided by Mammen, Marron, Turlach and Wand and
the asymptotic theory of our estimators is derived using the theory of additive
projections reviewed in Bickel, Klaassen, Ritov and Wellner. Our procedure
achieves the same bias and variance as the oracle estimator based on knowing
the other components, and in this sense improves on the method analyzed in
Opsomer and Ruppert. We provide ‘‘high level’’
conditions independent of the sampling scheme. We then verify that these
conditions are satisfied in a regression and a time series autoregression under
weak conditions.
Publié le : 1999-10-14
Classification:
Additive models,
alternating projections,
backfitting,
kernel smoothing,
local polynomials,
nonparametric regression,
62G07,
62G20
@article{1017939138,
author = {Mammen, E. and Linton, O. and Nielsen, J.},
title = {The existence and asymptotic properties of a backfitting
projection algorithm under weak conditions},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 1443-1490},
language = {en},
url = {http://dml.mathdoc.fr/item/1017939138}
}
Mammen, E.; Linton, O.; Nielsen, J. The existence and asymptotic properties of a backfitting
projection algorithm under weak conditions. Ann. Statist., Tome 27 (1999) no. 4, pp. 1443-1490. http://gdmltest.u-ga.fr/item/1017939138/