TY - JOUR
T1 - On sliced inverse regression with high-dimensional covariates
AU - ZHU, Lixing
AU - Miao, Baiqi
AU - PENG, Heng
N1 - Funding Information:
Lixing Zhu is Professor of Statistics, Department of Mathematics, Hong Kong Baptist University, and Cheung Kong Chair Professor at Renmin University of China under the Cheung Kong Scholars Program of the Ministry of Education and Li Ka Shing Foundation, Hong Kong, People’s Republic of China (E-mail: [email protected]). Baiqi Miao is Professor, University of Science and Technology of China. Heng Peng is Post-Doctoral Fellow, Princeton University, Princeton, NJ 08544. This research was supported by a grant from the University Grants Council of Hong Kong (HKU7181/02H). The authors are grateful to the editor, an associate editor, and the two referees for their constructive comments and suggestions, which led to the great improvement of earlier draft. They also thank the associate editor and one of the referees for their generous help in improving the presentation of the article.
PY - 2006/6
Y1 - 2006/6
N2 - Sliced inverse regression is a promising method for the estimation of the central dimension-reduction subspace (CDR space) in semiparametric regression models. It is particularly useful in tackling cases with high-dimensional covariates. In this article we study the asymptotic behavior of the estimate of the CDR space with high-dimensional covariates, that is. when the dimension of the covariates goes to infinity as the sample size goes to infinity. Strong and weak convergence are obtained. We also suggest an estimation procedure of the Bayes information criterion type to ascertain the dimension of the CDR space and derive the consistency. A simulation study is conducted.
AB - Sliced inverse regression is a promising method for the estimation of the central dimension-reduction subspace (CDR space) in semiparametric regression models. It is particularly useful in tackling cases with high-dimensional covariates. In this article we study the asymptotic behavior of the estimate of the CDR space with high-dimensional covariates, that is. when the dimension of the covariates goes to infinity as the sample size goes to infinity. Strong and weak convergence are obtained. We also suggest an estimation procedure of the Bayes information criterion type to ascertain the dimension of the CDR space and derive the consistency. A simulation study is conducted.
KW - Central dimension-reduction subspaee
KW - Convergence rate
KW - Dimensionality determination
KW - Sliced inverse regression
UR - http://www.scopus.com/inward/record.url?scp=33745658690&partnerID=8YFLogxK
U2 - 10.1198/016214505000001285
DO - 10.1198/016214505000001285
M3 - Journal article
AN - SCOPUS:33745658690
SN - 0162-1459
VL - 101
SP - 630
EP - 643
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 474
ER -