On a dimension reduction regression with covariate adjustment

Jun Zhang, Li Ping Zhu, Lixing ZHU*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

22 Citations (Scopus)


In this paper, we consider a semiparametric modeling with multi-indices when neither the response nor the predictors can be directly observed and there are distortions from some multiplicative factors. In contrast to the existing methods in which the response distortion deteriorates estimation efficacy even for a simple linear model, the dimension reduction technique presented in this paper interestingly does not have to account for distortion of the response variable. The observed response can be used directly whether distortion is present or not. The resulting dimension reduction estimators are shown to be consistent and asymptotically normal. The results can be employed to test whether the central dimension reduction subspace has been estimated appropriately and whether the components in the basis directions in the space are significant. Thus, the method provides an alternative for determining the structural dimension of the subspace and for variable selection. A simulation study is carried out to assess the performance of the proposed method. The analysis of a real dataset demonstrates the potential usefulness of distortion removal.

Original languageEnglish
Pages (from-to)39-55
Number of pages17
JournalJournal of Multivariate Analysis
Issue number1
Publication statusPublished - Feb 2012

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Central subspace
  • Covariate-adjusted regression
  • Dimension reduction


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