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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Bibliographic Details
Published inJournal of multivariate analysis Vol. 174; p. 104542
Main Authors Fan, Guo-Liang, Xu, Hong-Xia, Liang, Han-Ying
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2019
Subjects
Central mean subspace
High dimensionality
Missing data
Multivariate response
Sufficient dimension reduction
secondary
Missing data
Central mean subspace
Sufficient dimension reduction
High dimensionality
Multivariate response
primary
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Summary: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.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2019.104542