In many situations regression analysis is mostly concerned with
inferring about the conditional mean of the response given the predictors, and
less concerned with the other aspects of the conditional distribution. In this
paper we develop dimension reduction methods that incorporate this
consideration. We introduce the notion of the Central Mean Subspace (CMS), a
natural inferential object for dimension reduction when the mean function is of
interest. We study properties of the CMS, and develop methods to estimate it.
These methods include a new class of estimators which requires fewer conditions
than pHd, and which displays a clear advantage when one of the conditions for
pHd is violated. CMS also reveals a transparent distinction among the existing
methods for dimension reduction: OLS, pHd, SIR and SAVE. We apply the new
methods to a data set involving recumbent cows.
Publié le : 2002-04-14
Classification:
Central subspace,
graphics,
regression,
pHd,
SAVE,
SIR,
visualization,
62G08,
62-09,
62H05
@article{1021379861,
author = {Cook, R.Dennis and Li, Bing},
title = {Dimension reduction for conditional mean in regression},
journal = {Ann. Statist.},
volume = {30},
number = {1},
year = {2002},
pages = { 455-474},
language = {en},
url = {http://dml.mathdoc.fr/item/1021379861}
}
Cook, R.Dennis; Li, Bing. Dimension reduction for conditional mean in regression. Ann. Statist., Tome 30 (2002) no. 1, pp. 455-474. http://gdmltest.u-ga.fr/item/1021379861/