Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Intensive numerical studies of optimal sufficient dimension reduction with singularity

  • Yoo, Jae Keun (Department of Statistics, Ewha Womans University) ;
  • Gwak, Da-Hae (Department of Statistics, Ewha Womans University) ;
  • Kim, Min-Sun (Department of Statistics, Ewha Womans University)
  • Received : 2017.03.09
  • Accepted : 2017.05.15
  • Published : 2017.05.31
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Abstract

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 $x^2$ 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).

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References

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