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

Xiangrong Yin, Bing Li and R. Dennis Cook

Journal of Multivariate Analysis, 2008, vol. 99, issue 8, 1733-1757

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.

Keywords: primary; 62B05 secondary; 62H20 Dimension reduction subspaces Permutation test Regression graphics Sufficient dimension reduction (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (59)

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