TY - JOUR
T1 - On partial sufficient dimension reduction with applications to partially linear multi-index models
AU - Feng, Zhenghui
AU - Wen, Xuerong Meggie
AU - Yu, Zhou
AU - ZHU, Lixing
N1 - Funding Information:
Feng and Wen contributed equally to this work. Zhenghui Feng is Assistant Professor, School of Economics & Wang Yanan Institute for Studies in Economics (WISE), Xiamen University, Fujian Province, China (E-mail: [email protected]). Xuerong Meggie Wen is corresponding author and Associate Professor, Missouri University of Science and Technology, Rolla, MO 65409 (E-mail: [email protected]). Her work was supported by the Missouri Research Board. Zhou Yu is Assistant Professor, School of Finance and Statistics, East China Normal University, Shanghai, China (E-mail: [email protected]). His research was supported by a grant from the National Natural Science Foundation of China (no. 11201151). Lixing Zhu is Chair Professor, Department of Mathematics, Hong Kong Baptist University, Hong Kong, China (E-mail: [email protected]). His research was supported by a grant from the Research Grants Council of Hong Kong and a Faculty Research Grant (FRG) from Hong Kong Baptist University. The authors thank three anonymous referees, an associate editor, and the coeditor for their many constructive suggestions that helped us improve both the presentation and the substance of this article.
PY - 2013
Y1 - 2013
N2 - Partial dimension reduction is a general method to seek informative convex combinations of predictors of primary interest, which includes dimension reduction as its special case when the predictors in the remaining part are constants. In this article, we propose a novel method to conduct partial dimension reduction estimation for predictors of primary interest without assuming that the remaining predictors are categorical. To this end, we first take the dichotomization step such that any existing approach for partial dimension reduction estimation can be employed. Then we take the expectation step to integrate over all the dichotomic predictors to identify the partial central subspace. As an example, we use the partially linear multi-index model to illustrate its applications for semiparametric modeling. Simulations and real data examples are given to illustrate our methodology.
AB - Partial dimension reduction is a general method to seek informative convex combinations of predictors of primary interest, which includes dimension reduction as its special case when the predictors in the remaining part are constants. In this article, we propose a novel method to conduct partial dimension reduction estimation for predictors of primary interest without assuming that the remaining predictors are categorical. To this end, we first take the dichotomization step such that any existing approach for partial dimension reduction estimation can be employed. Then we take the expectation step to integrate over all the dichotomic predictors to identify the partial central subspace. As an example, we use the partially linear multi-index model to illustrate its applications for semiparametric modeling. Simulations and real data examples are given to illustrate our methodology.
KW - Partial central subspace
KW - Partial discretization-expectation estimation
KW - Partially linear model
UR - http://www.scopus.com/inward/record.url?scp=84878260235&partnerID=8YFLogxK
U2 - 10.1080/01621459.2012.746065
DO - 10.1080/01621459.2012.746065
M3 - Journal article
AN - SCOPUS:84878260235
SN - 0162-1459
VL - 108
SP - 237
EP - 246
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 501
ER -