Approximating conditional distribution functions using dimension reduction

• 成果类型: Article
• 署名作者: Hall, P; Yao, QW
• 署名单位: Australian National University; University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000001282
• 发表日期: 2005
• 页码: 1404-1421
• 关键词: single-index models; projection pursuit; DENSITY-ESTIMATION; time-series; regression; kernel; quantile

摘要

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 vertical bar X, but that of Y vertical bar theta(T)X' where the unit vector theta is selected so that the approximation is optimal under a least-squares criterion. We show that theta may be estimated root-n consistently, Furthermore, estimation of the conditional distribution function of Y, given theta(T)X, has the same first-order asymptotic properties that it would enjoy if theta 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 theta can be estimated particularly accurately.