Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of Y|X, but that of Y|θTX, where the unit vector θ is selected so that the approximation is optimal under a least-squares criterion. We show that θ may be estimated root-n consistently. Furthermore, estimation of the conditional distribution function of Y, given θTX, has the same first-order asymptotic properties that it would enjoy if θ were known. The proposed method is illustrated using both simulated and real-data examples, showing its effectiveness for both independent datasets and data from time series. Numerical work corroborates the theoretical result that θ can be estimated particularly accurately.
Publié le : 2005-06-14
Classification:
Conditional distribution,
cross-validation,
dimension reduction,
kernel methods,
leave-one-out method,
local linear regression,
nonparametric regression,
prediction,
root-n consistency,
time series analysis,
62E17,
62G05,
62G20
@article{1120224107,
author = {Hall, Peter and Yao, Qiwei},
title = {Approximating conditional distribution functions using dimension reduction},
journal = {Ann. Statist.},
volume = {33},
number = {1},
year = {2005},
pages = { 1404-1421},
language = {en},
url = {http://dml.mathdoc.fr/item/1120224107}
}
Hall, Peter; Yao, Qiwei. Approximating conditional distribution functions using dimension reduction. Ann. Statist., Tome 33 (2005) no. 1, pp. 1404-1421. http://gdmltest.u-ga.fr/item/1120224107/