Successive direction extraction for estimating the central subspace in a multiple-index regression

JOURNAL OF MULTIVARIATE ANALYSIS

卷:99

Article

Yin, Xiangrong¹  Li, Bing²  Cook, R. Dennis³ 

[1] Univ Georgia, Dept Stat, Athens, GA 30602 USA

[2] Penn State Univ, Dept Stat, University Pk, PA 16802 USA

[3] Univ Minnesota, Sch Stat, St Paul, MN 55455 USA

关键词: dimension reduction subspaces;    permutation test;    regression graphics;    sufficient dimension reduction;   

DOI  :  10.1016/j.jmva.2008.01.006

来源: Elsevier

【 摘 要 】

In this paper we propose a dimension reduction method for estimating the directions in a multiple-index regression based on information extraction. This extends the recent work of Yin and Cook [X. Yin, R.D. Cook, Direction estimation in single-index regression, Biometrika 92 (2005) 371-384] who introduced the method and used it to estimate the direction in a single-index regression. While a formal extension seems conceptually straightforward, there is a fundamentally new aspect of our extension: We are able to show that, under the assumption of elliptical predictors, the estimation of multiple-index regressions can be decomposed into successive single-index estimation problems. This significantly reduces the computational complexity, because the nonparametric procedure involves only a one-dimensional search at each stage. In addition, we developed a permutation test to assist in estimating the dimension of a multiple-index regression. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free