On robustness in dimension determination in fused sliced inverse regression

Jae Keun Yoo; Yoo Na Cho

doi:10.29220/CSAM.2018.25.5.513

On robustness in dimension determination in fused sliced inverse regression

Jae Keun Yoo, Yoo Na Cho

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	513-521
Number of pages	9
Journal	Communications for Statistical Applications and Methods
Volume	25
Issue number	5
DOIs	https://doi.org/10.29220/CSAM.2018.25.5.513
State	Published - 2018

Bibliographical note

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.

Keywords

Fused sliced inverse regression
Permutation test
Sufficient dimension reduction
central subspace

Access to Document

10.29220/CSAM.2018.25.5.513

Cite this

@article{21878ce3f75f4b2aabc7f6686efd3a55,

title = "On robustness in dimension determination in fused sliced inverse regression",

abstract = "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.",

keywords = "Fused sliced inverse regression, Permutation test, Sufficient dimension reduction, central subspace",

author = "Yoo, {Jae Keun} and Cho, {Yoo Na}",

note = "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: {\textcopyright} 2018 The Korean Statistical Society, and Korean International Statistical Society.",

year = "2018",

doi = "10.29220/CSAM.2018.25.5.513",

language = "English",

volume = "25",

pages = "513--521",

journal = "Communications for Statistical Applications and Methods",

issn = "2287-7843",

publisher = "Korean Statistical Society",

number = "5",

}

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 -

On robustness in dimension determination in fused sliced inverse regression

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this