Sufficient dimension reduction through discretization-expectation estimation

Liping Zhu, Tao Wang, Lixing ZHU, Louis Ferré

Research output: Contribution to journalArticlepeer-review

71 Citations (Scopus)

Abstract

In the context of sufficient dimension reduction, the goal is to parsimoniously recover the central subspace of a regression model. Many inverse regression methods use slicing estimation to recover the central subspace. The efficacy of slicing estimation depends heavily upon the number of slices. However, the selection of the number of slices is an open and long-standing problem. In this paper, we propose a discretization-expectation estimation method, which avoids selecting the number of slices, while preserving the integrity of the central subspace. This generic method assures root-n consistency and asymptotic normality of slicing estimators for many inverse regression methods, and can be applied to regressions with multivariate responses. A BIC-type criterion for the dimension of the central subspace is proposed. Comprehensive simulations and an illustrative application show that our method compares favourably with existing estimators.

Original languageEnglish
Pages (from-to)295-304
Number of pages10
JournalBiometrika
Volume97
Issue number2
DOIs
Publication statusPublished - Jun 2010

Scopus Subject Areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

User-Defined Keywords

  • Binary response
  • Central subspace
  • Dimension reduction
  • Graphical regression
  • Sliced inverse regression

Fingerprint

Dive into the research topics of 'Sufficient dimension reduction through discretization-expectation estimation'. Together they form a unique fingerprint.

Cite this