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

Xiangrong Yin, Bing Li, R. Dennis Cook

Research output: Contribution to journalArticle

97 Scopus citations

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 languageEnglish (US)
Pages (from-to)1733-1757
Number of pages25
JournalJournal of Multivariate Analysis
Volume99
Issue number8
DOIs
StatePublished - Sep 1 2008

Keywords

  • 62B05
  • 62H20
  • Dimension reduction subspaces
  • Permutation test
  • Regression graphics
  • Sufficient dimension reduction
  • primary
  • secondary

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