On cross-distance selection algorithm for hybrid sufficient dimension reduction

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Given the extensive development of a variety of sufficient dimension reduction (SDR) methodologies, Ye and Weiss (2003) proposed a hybrid SDR method combining two pre-existing SDR methods. In particular, they used a bootstrap approach to select a proper weight. Since bootstrapping is computationally intensive and time-consuming, the hybrid reduction approach has not been widely used, although it is more accurate than conventional single SDR methods. To overcome these deficits, we propose a novel cross-distance selection algorithm. Similar to the bootstrapping method, the proposed selection algorithm is data-driven and has a strong rationale for its performance. The numerical studies demonstrate that the chosen hybrid method from our proposed algorithm offers a good estimation quality and reduces the computing time dramatically at the same time. Furthermore, our real data analysis confirms that the proposed selection algorithm has potential advantages with its practical usefulness over the existing bootstrapping method.

Original languageEnglish
Article number107562
JournalComputational Statistics and Data Analysis
StatePublished - Dec 2022

Bibliographical note

Funding Information:
For Jae Keun Yoo, this work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education ( NRF-2021R1F1A1059844 ). For Kyongwon Kim, this work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIT ) (No. 2021R1F1A1046976 ). This research was also supported by the MSIT (Ministry of Science, ICT), Korea, under the High-Potential Individuals Global Training Program ( RS-2022-00154879 ) supervised by the IITP (Institute for Information & Communications Technology Planning & Evaluation).

Publisher Copyright:
© 2022 Elsevier B.V.


  • Covariance methods
  • Directional regression
  • Hybrid dimension reduction
  • Sliced average variance estimation
  • Sliced inverse regression
  • Sufficient dimension reduction


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