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June 2005 Approximating conditional distribution functions using dimension reduction
Peter Hall, Qiwei Yao
Ann. Statist. 33(3): 1404-1421 (June 2005). DOI: 10.1214/009053604000001282


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 YTX, 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.


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Peter Hall. Qiwei Yao. "Approximating conditional distribution functions using dimension reduction." Ann. Statist. 33 (3) 1404 - 1421, June 2005.


Published: June 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1072.62008
MathSciNet: MR2195640
Digital Object Identifier: 10.1214/009053604000001282

Primary: 62E17
Secondary: 62G05 , 62G20

Keywords: conditional distribution , cross-validation , Dimension reduction , kernel methods , leave-one-out method , local linear regression , Nonparametric regression , prediction , root-n consistency , time series analysis

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 3 • June 2005
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