Dimension reduction estimation for central mean subspace with missing multivariate response
Multivariate response data often arise in practice and they are frequently subject to missingness. Under this circumstance, the standard sufficient dimension reduction (SDR) methods cannot be used directly. To reduce the dimension and estimate the central mean subspace, a profile least squares estim...
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| Published in | Journal of multivariate analysis Vol. 174; p. 104542 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.11.2019
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| Online Access | Get full text |
| ISSN | 0047-259X 1095-7243 |
| DOI | 10.1016/j.jmva.2019.104542 |
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| Abstract | Multivariate response data often arise in practice and they are frequently subject to missingness. Under this circumstance, the standard sufficient dimension reduction (SDR) methods cannot be used directly. To reduce the dimension and estimate the central mean subspace, a profile least squares estimation method is proposed based on an inverse probability weighted technique. The profile least squares method does not need any distributional assumptions on the covariates and hence differs from existing SDR methods. The resulting estimator of the central mean subspace is proved to be asymptotically normal and root n consistent under some mild conditions. The structural dimension is determined by a BIC-type criterion and the consistency of its estimator is established. Comprehensive simulations and a real data analysis show that the proposed method works promisingly. |
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| AbstractList | Multivariate response data often arise in practice and they are frequently subject to missingness. Under this circumstance, the standard sufficient dimension reduction (SDR) methods cannot be used directly. To reduce the dimension and estimate the central mean subspace, a profile least squares estimation method is proposed based on an inverse probability weighted technique. The profile least squares method does not need any distributional assumptions on the covariates and hence differs from existing SDR methods. The resulting estimator of the central mean subspace is proved to be asymptotically normal and root n consistent under some mild conditions. The structural dimension is determined by a BIC-type criterion and the consistency of its estimator is established. Comprehensive simulations and a real data analysis show that the proposed method works promisingly. |
| ArticleNumber | 104542 |
| Author | Fan, Guo-Liang Xu, Hong-Xia Liang, Han-Ying |
| Author_xml | – sequence: 1 givenname: Guo-Liang surname: Fan fullname: Fan, Guo-Liang organization: School of Economics and Management, Shanghai Maritime University, Shanghai, 201306, PR China – sequence: 2 givenname: Hong-Xia surname: Xu fullname: Xu, Hong-Xia organization: Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, PR China – sequence: 3 givenname: Han-Ying surname: Liang fullname: Liang, Han-Ying email: hyliang@tongji.edu.cn organization: School of Mathematical Sciences, Tongji University, Shanghai 200092, PR China |
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| Title | Dimension reduction estimation for central mean subspace with missing multivariate response |
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