Dimension reduction regressions with measurement errors subject to additive distortion

ABSTRACT

In this paper, we propose several dimension reduction methods when the covariates are measured with additive distortion measurement errors. These distortions are modelled by unknown functions of a commonly observable confounding variable. To estimate the central subspace, we propose residuals-based dimension reduction estimation methods and direct estimation methods. The consistency and asymptotic normality of the proposed estimators are investigated. Furthermore, we conduct some simulations to evaluate the performance of our proposed method and compare with existing methods, and a real data set is analysed for illustration.

KEYWORDS:

• Dimension reduction
• measurement errors
• additive distortion
• eigen-decomposition

MATHEMATICS SUBJECT CLASSIFICATION (2000):

• 62G05
• 62G08
• 62G20

Acknowledgements

The authors thank the editor, the associate editor and a referee for their constructive suggestions that helped them to improve the early manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jun Zhang   http://orcid.org/0000-0003-4332-5182

Additional information

Funding

Junhua Zhang's research was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11472057), Qinxin Talents Cultivation Program of Beijing Information Science and Technology University (No. QXTCPB201701) and Beijing Natural Science Foundation (No. 1182010). Bingqing Lin's research was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11701386). Yan Zhou's research was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11701385), National Statistical Research Project (Grant No. 2017LY56) and Doctor start fund of Guangdong Province (Grant No. 2016A030310062).