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More on directional regression
Communications for Statistical Applications and Methods 2021;28:553-562
Published online September 30, 2021
© 2021 Korean Statistical Society.

Kyongwon Kim1,a, Jae Keun Yoo2,a

aDepartment of Statistics, Ewha Womans University, Korea
Correspondence to: 1 Department of Statistics, Ewha Womans University, 52, Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Korea. E-mail: kimk@ewha.ac.kr
2 Departmentof Statistics, Ewha Womans University, 52, Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Korea. E-mail: peter.yoo@ewha.ac.kr
Received May 5, 2021; Revised May 24, 2021; Accepted May 24, 2021.
 Abstract
Directional regression (DR; Li and Wang, 2007) is well-known as an exhaustive sucient dimension reduction method, and performs well in complex regression models to have linear and nonlinear trends. However, the extension of DR is not well-done upto date, so we will extend DR to accommodate multivariate regression and large p-small n regression. We propose three versions of DR for multivariate regression and discuss how DR is applicable for the latter regression case. Numerical studies confirm that DR is robust to the number of clusters and the choice of hierarchical-clustering or pooled DR.
Keywords : central subspace, fused sliced inverse regression, multivariate regression, pooled approach, sufficient dimension reduction