On a dimension reduction regression with covariate adjustment

JOURNAL OF MULTIVARIATE ANALYSIS

卷:104

Article

Zhang, Jun²  Zhu, Li-Ping²  Zhu, Li-Xing¹ 

[1] Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China

[2] E China Normal Univ, Sch Finance & Stat, Shanghai 200062, Peoples R China

关键词: Central subspace;    Covariate-adjusted regression;    Dimension reduction;   

DOI  :  10.1016/j.jmva.2011.06.004

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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