TY - JOUR
T1 - Response dimension reduction for the conditional mean in multivariate regression
AU - Yoo, Jae Keun
AU - Cook, R. Dennis
N1 - Funding Information:
The authors are grateful to the referees for many helpful comments. The second author was supported in part by National Science Foundation Grant DMS-0405360.
PY - 2008/12/15
Y1 - 2008/12/15
N2 - Sufficient dimension reduction methodologies in regression have been developed in the past decade, focusing mostly on predictors. Here, we propose a methodology to reduce the dimension of the response vector in multivariate regression, without loss of information about the conditional mean. The asymptotic distributions of dimension test statistics are chi-squared distributions, and an estimate of the dimension reduction subspace is asymptotically efficient. Moreover, the proposed methodology enables us to test response effects for the conditional mean. Properties of the proposed method are studied via simulation.
AB - Sufficient dimension reduction methodologies in regression have been developed in the past decade, focusing mostly on predictors. Here, we propose a methodology to reduce the dimension of the response vector in multivariate regression, without loss of information about the conditional mean. The asymptotic distributions of dimension test statistics are chi-squared distributions, and an estimate of the dimension reduction subspace is asymptotically efficient. Moreover, the proposed methodology enables us to test response effects for the conditional mean. Properties of the proposed method are studied via simulation.
UR - http://www.scopus.com/inward/record.url?scp=55549128558&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2008.07.029
DO - 10.1016/j.csda.2008.07.029
M3 - Article
AN - SCOPUS:55549128558
SN - 0167-9473
VL - 53
SP - 334
EP - 343
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 2
ER -