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

Authors:
Xiangrong Yin;Bing Li;R. Dennis Cook
Affiliations:
Department of Statistics, 204 Statistics Building, University of Georgia, Athens, GA 30602, United States;Department of Statistics, Penn State University, 326 Thomas Building, University Park, PA 16802, United States;School of Statistics, 224 Church Street, S.E., 313 Ford Hall, University of Minnesota, St. Paul, MN 55455, United States
Venue:
Journal of Multivariate Analysis
Year:
2008

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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.