The Annals of Statistics
- Ann. Statist.
- Volume 33, Number 3 (2005), 1404-1421.
Approximating conditional distribution functions using dimension reduction
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.
Ann. Statist., Volume 33, Number 3 (2005), 1404-1421.
First available in Project Euclid: 1 July 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 62G05: Estimation 62G20: Asymptotic properties
Conditional distribution cross-validation dimension reduction kernel methods leave-one-out method local linear regression nonparametric regression prediction root-n consistency time series analysis
Hall, Peter; Yao, Qiwei. Approximating conditional distribution functions using dimension reduction. Ann. Statist. 33 (2005), no. 3, 1404--1421. doi:10.1214/009053604000001282. https://projecteuclid.org/euclid.aos/1120224107