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On robustness in dimension determination in fused sliced inverse regression
Commun. Stat. Appl. Methods, CSAM 2018;25:513-521
Published online September 30, 2018
© 2018 Korean Statistical Society.

Jae Keun Yoo1,a, Yoo Na Choa

aDepartment of Statistics, Ewha Womans University, Korea
Correspondence to: Department of Statistics, Ewha Womans University, 52, Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Korea. E-mail: peter.yoo@ewha.ac.kr
Received March 9, 2018; Revised May 11, 2018; Accepted May 13, 2018.
 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 : central subspace, fused sliced inverse regression, permutation test, sufficient dimension reduction