Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Note on response dimension reduction for multivariate regression

  • Yoo, Jae Keun (Department of Statistics, Ewha Womans University)
  • Received : 2019.07.19
  • Accepted : 2019.08.30
  • Published : 2019.09.30
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Abstract

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.

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References

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