TY - JOUR
T1 - On robustness in dimension determination in fused sliced inverse regression
AU - Yoo, Jae Keun
AU - Cho, Yoo Na
N1 - Funding Information:
The authors are grateful to two reviewers and the Associate Editor for insightful comments to improve the paper. For Jae Keun Yoo, this work was supported by Basic Science Research Program of the National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education (NRF-2017R1A2B1004909and 2009-0093827). For YuNa Cho, this work was supported by the BK21 Plus Project of National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education (22A20130011003).
Funding Information:
The authors are grateful to two reviewers and the Associate Editor for insightful comments to improve the paper. For Jae Keun Yoo, this work was supported by Basic Science Research Program of the National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education (NRF-2017R1A2B1004909and 2009-0093827). For YuNa Cho, this work was supported by the BK21 Plus Project of National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education (22A20130011003)
Publisher Copyright:
© 2018 The Korean Statistical Society, and Korean International Statistical Society.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Fused sliced inverse regression
KW - Permutation test
KW - Sufficient dimension reduction
KW - central subspace
UR - http://www.scopus.com/inward/record.url?scp=85057415634&partnerID=8YFLogxK
U2 - 10.29220/CSAM.2018.25.5.513
DO - 10.29220/CSAM.2018.25.5.513
M3 - Article
AN - SCOPUS:85057415634
SN - 2287-7843
VL - 25
SP - 513
EP - 521
JO - Communications for Statistical Applications and Methods
JF - Communications for Statistical Applications and Methods
IS - 5
ER -