Approximating conditional distribution functions using dimension reduction
| dc.creator | Hall, Peter | |
| dc.creator | Yao, Qiwei | |
| dc.date | 2005-07-21 | |
| dc.date.accessioned | 2026-07-07T08:07:05Z | |
| dc.date.available | 2026-07-07T08:07:05Z | |
| dc.description | 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|θ^TX, where the unit vector θis selected so that the approximation is optimal under a least-squares criterion. We show that θmay be estimated root-n consistently. Furthermore, estimation of the conditional distribution function of Y, given θ^TX, has the same first-order asymptotic properties that it would enjoy if θwere 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 θcan be estimated particularly accurately. | |
| dc.description | Published at http://dx.doi.org/10.1214/009053604000001282 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0507432 | |
| dc.identifier | http://arxiv.org/abs/math/0507432 | |
| dc.identifier | Annals of Statistics 2005, Vol. 33, No. 3, 1404-1421 | |
| dc.identifier | doi:10.1214/009053604000001282 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130825 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62E17 (Primary) 62G05\sep62G20 (Secondary) | |
| dc.title | Approximating conditional distribution functions using dimension reduction | |
| dc.type | text |