Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Iterative projection of sliced inverse regression with fused approach

  • Han, Hyoseon (Department of Statistics, Ewha Womans University) ;
  • Cho, Youyoung (Department of Statistics, Ewha Womans University) ;
  • Yoo, Jae Keun (Department of Statistics, Ewha Womans University)
  • Received : 2020.12.28
  • Accepted : 2021.02.01
  • Published : 2021.03.31
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Abstract

Sufficient dimension reduction is useful dimension reduction tool in regression, and sliced inverse regression (Li, 1991) is one of the most popular sufficient dimension reduction methodologies. In spite of its popularity, it is known to be sensitive to the number of slices. To overcome this shortcoming, the so-called fused sliced inverse regression is proposed by Cook and Zhang (2014). Unfortunately, the two existing methods do not have the direction application to large p-small n regression, in which the dimension reduction is desperately needed. In this paper, we newly propose seeded sliced inverse regression and seeded fused sliced inverse regression to overcome this deficit by adopting iterative projection approach (Cook et al., 2007). Numerical studies are presented to study their asymptotic estimation behaviors, and real data analysis confirms their practical usefulness in high-dimensional data analysis.

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Acknowledgement

For Jae Keun Yoo, this work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education (NRF-2019R1F1A1050715).

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