On robustness in dimension determination in fused sliced inverse regression

Jae Keun Yoo, Yoo Na Cho

Research output: Contribution to journalArticlepeer-review


The goal of sufficient dimension reduction (SDR) is to replace original p-dimensional predictors with a lower-dimensional linearly transformed predictor. The sliced inverse regression (SIR) (Li, Journal of the American Statistical Association, 86, 316-342, 1991) is one of the most popular SDR methods because of its applicability and simple implementation in practice. However, SIR may yield different dimension reduction results for different numbers of slices and despite its popularity, is a clear deficit for SIR. To overcome this, a fused sliced inverse regression was recently proposed. The study shows that the dimension-reduced predictors is robust to the numbers of the slices, but it does not investigate how robust its dimension determination is. This paper suggests a permutation dimension determination for the fused sliced inverse regression that is compared with SIR to investigate the robustness to the numbers of slices in the dimension determination. Numerical studies confirm this and a real data example is presented.

Original languageEnglish
Pages (from-to)513-521
Number of pages9
JournalCommunications for Statistical Applications and Methods
Issue number5
StatePublished - 2018

Bibliographical note

Publisher Copyright:
© 2018 The Korean Statistical Society, and Korean International Statistical Society.


  • Fused sliced inverse regression
  • Permutation test
  • Sufficient dimension reduction
  • central subspace


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