Two variations of cross-distance selection algorithm in hybrid sufficient dimension reduction

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Hybrid sufficient dimension reduction (SDR) methods to a weighted mean of kernel matrices of two different SDR methods by Ye and Weiss (2003) require heavy computation and time consumption due to bootstrapping. To avoid this, Park et al. (2022) recently develop the so-called cross-distance selection (CDS) algorithm. In this paper, two variations of the original CDS algorithm are proposed depending on how well and equally the covk-SAVE is treated in the selection procedure. In one variation, which is called the larger CDS algorithm, the covk-SAVE is equally and fairly utilized with the other two candiates of SIR-SAVE and covk-DR. But, for the final selection, a random selection should be necessary. On the other hand, SIR-SAVE and covk-DR are utilized with completely ruling covk-SAVE out, which is called the smaller CDS algorithm. Numerical studies confirm that the original CDS algorithm is better than or compete quite well to the two proposed variations. A real data example is presented to compare and interpret the decisions by the three CDS algorithms in practice.

Original languageEnglish
Pages (from-to)179-189
Number of pages11
JournalCommunications for Statistical Applications and Methods
Issue number2
StatePublished - 2023

Bibliographical note

Funding Information:
For Jae Keun Yoo, this work was supported by Basic Science Research Program through the National Research Founda-tion of Korea (NRF) funded by the Korean Ministry of Education (NRF-2021R1F1A1059844). 1 Corresponding Author: Department of Statistics, Ewha Womans University, 11-1 Daehyun-Dong Seodaemun-Gu, Seoul 03760, Korea. E-mail:

Publisher Copyright:
© 2023 The Korean Statistical Society, and Korean International Statistical Society. All rights reserved. All Rights Reserved.


  • basis-adaptive selection
  • cross-distance selection
  • hybrid dimension reduction
  • suffi-cient dimension reduction
  • trace correlation


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