Intensive numerical studies of optimal sufficient dimension reduction with singularity

Jae Keun Yoo, Da Hae Gwak, Min Sun Kim

Research output: Contribution to journalArticlepeer-review


Yoo (2015, Statistics and Probability Letters, 99, 109-113) derives theoretical results in an optimal sufficient dimension reduction with singular inner-product matrix. The results are promising, but Yoo (2015) only presents one simulation study. So, an evaluation of its practical usefulness is necessary based on numerical studies. This paper studies the asymptotic behaviors of Yoo (2015) through various simulation models and presents a real data example that focuses on ordinary least squares. Intensive numerical studies show that the X2 test by Yoo (2015) outperforms the existing optimal sufficient dimension reduction method. The basis estimation by the former can be theoretically sub-optimal; however, there are no notable differences from that by the latter. This investigation confirms the practical usefulness of Yoo (2015).

Original languageEnglish
Pages (from-to)303-315
Number of pages13
JournalCommunications for Statistical Applications and Methods
Issue number3
StatePublished - 1 May 2017


  • Chi-square test
  • Optimality
  • Singularity
  • Sufficient dimension reduction


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