Flexible dimension reduction in regression

Tao Wang, Lixing ZHU

Research output: Contribution to journalEditorial

Abstract

Sliced inverse regression is a valuable tool for dimension reduction. One can replace the predictor vector with a few linear combinations of its components without loss of information on the regression. This paper is about richer nonlinear dimension reduction. Each direction of sliced inverse regression is simply a slope vector of multiple linear regression applied to an optimally transformed response. Using this connection, we propose a nonlinear version of sliced inverse regression by replacing linear function by an additive function of the predictors. Our procedure has a clear interpretation as sliced inverse regression on a set of adaptively chosen transformations of the predictors. The flexibility of our method is illustrated via a simulation study and a data application.

Original languageEnglish
Pages (from-to)1009-1029
Number of pages21
JournalStatistica Sinica
Volume28
Issue number2
DOIs
Publication statusPublished - Apr 2018

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Canonical correlation
  • Optimal scoring
  • Sufficient dimension reduction

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