TY - JOUR
T1 - Successive direction extraction for estimating the central subspace in a multiple-index regression
AU - Yin, Xiangrong
AU - Li, Bing
AU - Cook, R. Dennis
N1 - 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.
PY - 2008/9
Y1 - 2008/9
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jmva.2008.01.006
DO - 10.1016/j.jmva.2008.01.006
M3 - Article
AN - SCOPUS:48749099148
SN - 0047-259X
VL - 99
SP - 1733
EP - 1757
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 8
ER -