Dimension reduction estimation for central mean subspace with missing multivariate response

JOURNAL OF MULTIVARIATE ANALYSIS

卷:174

Article

Fan, Guo-Liang¹  Xu, Hong-Xia²  Liang, Han-Ying³ 

[1] Shanghai Maritime Univ, Sch Econ & Management, Shanghai 201306, Peoples R China

[2] Shanghai Maritime Univ, Dept Math, Shanghai 201306, Peoples R China

[3] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

关键词: Central mean subspace;    High dimensionality;    Missing data;    Multivariate response;    Sufficient dimension reduction;   

DOI  :  10.1016/j.jmva.2019.104542

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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