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Approximating conditional distribution functions using dimension reduction

Hall, Peter; Yao, Qiwei


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...[Show more]

CollectionsANU Research Publications
Date published: 2005-07-21
Type: Journal article
Source: Annals of Statistics
DOI: 10.1214/009053604000001282


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