Data-driven slicing for dimension reduction in regressions: A likelihood-ratio approach

Peirong Xu, Tao Wang*, Lixing Zhu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


To efficiently estimate the central subspace in sufficient dimension reduction, response discretization via slicing its range is one of the most used methodologies when inverse regression-based methods are applied. However, existing slicing schemes are almost all ad hoc and not widely accepted. Thus, how to define data-driven schemes with certain optimal properties is a longstanding problem in this field. The research described herewith is then two-fold. First, we introduce a likelihood-ratio-based framework for dimension reduction, subsuming the popularly used methods including the sliced inverse regression, the sliced average variance estimation and the likelihood acquired direction. Second, we propose a regularized log likelihood-ratio criterion to obtain a data-driven slicing scheme and derive the asymptotic properties of the estimators. A simulation study is carried out to examine the performance of the proposed method and that of existing methods. A data set concerning concrete compressive strength is also analyzed for illustration and comparison.

Original languageEnglish
Pages (from-to)647–664
Number of pages18
JournalScience China Mathematics
Issue number3
Early online date29 Aug 2023
Publication statusPublished - Mar 2024

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • 62H25
  • 62J02
  • adaptive slicing
  • full-likelihood approach
  • regularization
  • second-order method


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