Note on response dimension reduction for multivariate regression

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Response dimension reduction in a sufficient dimension reduction (SDR) context has been widely ignored until Yoo and Cook (Computational Statistics and Data Analysis, 53, 334�343, 2008) founded theories for it and developed an estimation approach. Recent research in SDR shows that a semi-parametric approach can outperform conventional non-parametric SDR methods. Yoo (Statistics: A Journal of Theoretical and Applied Statistics, 52, 409�425, 2018) developed a semi-parametric approach for response reduction in Yoo and Cook (2008) context, and Yoo (Journal of the Korean Statistical Society, 2019) completes the semi-parametric approach by proposing an unstructured method. This paper theoretically discusses and provides insightful remarks on three versions of semi-parametric approaches that can be useful for statistical practitioners. It is also possible to avoid numerical instability by presenting the results for an orthogonal transformation of the response variables.

Original languageEnglish
Pages (from-to)519-526
Number of pages8
JournalCommunications for Statistical Applications and Methods
Issue number5
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019 The Korean Statistical Society, and Korean International Statistical Society. All rights reserved.


  • Conditional mean
  • Multivariate regression
  • Response dimension reduction
  • Semi-parametric model
  • Sufficient dimension reduction


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