Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1733-1757 |
| Number of pages | 25 |
| Journal | Journal of Multivariate Analysis |
| Volume | 99 |
| Issue number | 8 |
| DOIs | |
| State | Published - Sep 2008 |
Bibliographical note
Funding Information:The second author’s work is supported in part by National Science Foundation grants DMS-0204662 and DMS-0405681. He would like to thank Anand Vidyashankar for support for visiting UGA where part of this work was done.
Funding Information:
The third author’s work was supported in part by National Science Foundation grants DMS-0405360 and 0704098.
Keywords
- 62B05
- 62H20
- Dimension reduction subspaces
- Permutation test
- Regression graphics
- Sufficient dimension reduction
- primary
- secondary