TY - JOUR
T1 - Note on response dimension reduction for multivariate regression
AU - Yoo, Jae Keun
N1 - 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-2019R1F1A1050715).
Publisher Copyright:
© 2019 The Korean Statistical Society, and Korean International Statistical Society. All rights reserved.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Conditional mean
KW - Multivariate regression
KW - Response dimension reduction
KW - Semi-parametric model
KW - Sufficient dimension reduction
UR - http://www.scopus.com/inward/record.url?scp=85074632127&partnerID=8YFLogxK
U2 - 10.29220/CSAM.2019.26.5.519
DO - 10.29220/CSAM.2019.26.5.519
M3 - Article
AN - SCOPUS:85074632127
SN - 2287-7843
VL - 26
SP - 519
EP - 526
JO - Communications for Statistical Applications and Methods
JF - Communications for Statistical Applications and Methods
IS - 5
ER -