Approximating conditional distribution functions using dimension reduction

dc.creatorHall, Peter
dc.creatorYao, Qiwei
dc.date2005-07-21
dc.date.accessioned2026-07-07T08:07:05Z
dc.date.available2026-07-07T08:07:05Z
dc.descriptionMotivated 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.descriptionPublished 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.identifierhttps://arxiv.org/abs/math/0507432
dc.identifierhttp://arxiv.org/abs/math/0507432
dc.identifierAnnals of Statistics 2005, Vol. 33, No. 3, 1404-1421
dc.identifierdoi:10.1214/009053604000001282
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130825
dc.subjectStatistics Theory
dc.subject62E17 (Primary) 62G05\sep62G20 (Secondary)
dc.titleApproximating conditional distribution functions using dimension reduction
dc.typetext

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