TY - JOUR
T1 - Response dimension reduction
T2 - model-based approach
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-2012R1A1A1040077 and 2009-0093827].
Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2018/3/4
Y1 - 2018/3/4
N2 - In this paper, a model-based approach to reduce the dimension of response variables in multivariate regression is newly proposed, following the existing context of the response dimension reduction developed by Yoo and Cook [Response dimension reduction for the conditional mean in multivariate regression. Comput Statist Data Anal. 2008;53:334–343]. The related dimension reduction subspace is estimated by maximum likelihood, assuming an additive error. In the new approach, the linearity condition, which is assumed for the methodological development in Yoo and Cook (2008), is understood through the covariance matrix of the random error. Numerical studies show potential advantages of the proposed approach over Yoo and Cook (2008). A real data example is presented for illustration.
AB - In this paper, a model-based approach to reduce the dimension of response variables in multivariate regression is newly proposed, following the existing context of the response dimension reduction developed by Yoo and Cook [Response dimension reduction for the conditional mean in multivariate regression. Comput Statist Data Anal. 2008;53:334–343]. The related dimension reduction subspace is estimated by maximum likelihood, assuming an additive error. In the new approach, the linearity condition, which is assumed for the methodological development in Yoo and Cook (2008), is understood through the covariance matrix of the random error. Numerical studies show potential advantages of the proposed approach over Yoo and Cook (2008). A real data example is presented for illustration.
KW - Envelope
KW - Grassmann manifold
KW - multivariate regression
KW - response dimension reduction
KW - sufficient dimension reduction
UR - http://www.scopus.com/inward/record.url?scp=85043597351&partnerID=8YFLogxK
U2 - 10.1080/02331888.2017.1410152
DO - 10.1080/02331888.2017.1410152
M3 - Article
AN - SCOPUS:85043597351
SN - 0233-1888
VL - 52
SP - 409
EP - 425
JO - Statistics
JF - Statistics
IS - 2
ER -