TY - JOUR
T1 - On a projective resampling method for dimension reduction with multivariate responses
AU - Li, Bing
AU - Wen, Songqiao
AU - Zhu, Lixing
AU - Kong, Cheung
N1 - Funding Information:
Bing Li is Professor, Department of Statistics, Pennsylvania State University, University Park, PA 16802 (E-mail: bing@stat.psu.edu). Songqiao Wen is Ph.D. Student, Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (E-mail: sqwen@math.hkbu.edu.hk). Lixing Zhu is Professor, Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (E-mail: lzhu@hkbu.edu.hk) and Cheung Kong Chair Professor, Renmin University, Beijing, China. Li’s research is supported in part by grants DMS-0405681 and DMS-0704621 of the National Science Foundation. Zhu’s research is supported in part by a grant from the Research Grants Council of Hong Kong, Hong Kong, China. We thank two referees and an associate editor for their exceptionally careful and insightful comments, which have helped us to improve the contents and presentation of an earlier manuscript.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/9
Y1 - 2008/9
N2 - Consider the dimension reduction problem where both the response and the predictor are vectors. Existing estimators of this problem take one of the following routes: (1) targeting the part of the dimension reduction space that is related to the conditional mean (or moments) of the response vector, (2) pooling the estimates for the marginal dimension reduction spaces, and (3) estimating the whole dimension reduction space directly by multivariate slicing. However, the first two approaches do not fully recover the dimension reduction space, and the third is hampered by the fact that the accuracy of estimators based on multivariate slicing drops sharply as the dimension of response increases-a phenomenon often called the "curse of dimensionality." We propose a new method that overcomes both difficulties, in that it involves univariate slicing only and it is guaranteed to fully recover the dimension reduction space under reasonable conditions. The method will be compared with the existing estimators by simulation and applied to a dataset.
AB - Consider the dimension reduction problem where both the response and the predictor are vectors. Existing estimators of this problem take one of the following routes: (1) targeting the part of the dimension reduction space that is related to the conditional mean (or moments) of the response vector, (2) pooling the estimates for the marginal dimension reduction spaces, and (3) estimating the whole dimension reduction space directly by multivariate slicing. However, the first two approaches do not fully recover the dimension reduction space, and the third is hampered by the fact that the accuracy of estimators based on multivariate slicing drops sharply as the dimension of response increases-a phenomenon often called the "curse of dimensionality." We propose a new method that overcomes both difficulties, in that it involves univariate slicing only and it is guaranteed to fully recover the dimension reduction space under reasonable conditions. The method will be compared with the existing estimators by simulation and applied to a dataset.
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U2 - 10.1198/016214508000000445
DO - 10.1198/016214508000000445
M3 - Article
AN - SCOPUS:54949122171
SN - 0162-1459
VL - 103
SP - 1177
EP - 1186
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 483
ER -