Ultrahigh-dimensional sufficient dimension reduction for censored data with measurement error in covariates

Abstract

In this paper, we consider the ultrahigh-dimensional sufficient dimension reduction (SDR) for censored data and measurement error in covariates. We first propose the feature screening procedure based on censored data and the covariates subject to measurement error. With the suitable correction of mismeasurement, the error-contaminated variables detected by the proposed feature screening procedure are the same as the truly important variables. Based on the selected active variables, we develop the SDR method to estimate the central subspace and the structural dimension with both censored data and measurement error incorporated. The theoretical results of the proposed method are established. Simulation studies are reported to assess the performance of the proposed method. The proposed method is implemented to NKI breast cancer data.

Keywords:

• Cumulative mean estimation
• dimension reduction
• distance correlation
• feature screening
• measurement error
• survival data
• ultrahigh-dimension

2010 Mathematics Subject Classifications:

• 62N01
• 62N02

Acknowledgements

The author would like to extend great gratitude to the Editor, Associate Editor and two referees for their valuable suggestions and useful comments to make this paper better.

Disclosure statement

No potential conflict of interest was reported by the author(s).