On dimension reduction in regressions with multivariate responses

Li Ping Zhu*, Lixing Zhu, Song Qiao Wen

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

20 Citations (Scopus)


This paper is concerned with dimension reduction in regressions with multivariate responses on high-dimensional predictors. A unified method that can be regarded as either an inverse regression approach or a forward regression method is proposed to recover the central dimension reduction subspace. By using Stein's Lemma, the forward regression estimates the first derivative of the conditional characteristic function of the response given the predictors; by using the Fourier method, the inverse regression estimates the subspace spanned by the conditional mean of the predictors given the responses. Both methods lead to an identical kernel matrix, while preserving as much regression information as possible. Illustrative examples of a data set and comprehensive simulations are used to demonstrate the application of our methods.

Original languageEnglish
Pages (from-to)1291-1307
Number of pages17
JournalStatistica Sinica
Issue number3
Publication statusPublished - Jul 2010

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Central subspace
  • Dimension reduction
  • Ellipticity
  • Inverse regression
  • Multivariate response


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