The LAD estimation of the change-point linear model with randomly censored data

Abstract

In this paper, a change-point linear model with randomly censored data is investigated. We propose the least absolute deviation estimation procedure for regression and change-point parameters simultaneously. The asymptotic properties of the change-point and regression parameter estimators are obtained. We show that the resulting regression parameter estimator is asymptotically normal, and the change-point estimator converges weakly to the minimizer of a given random process. The extensive simulation studies and the analysis of an acute myocardial infarction data set are conducted to illustrate the finite sample performance of the proposed method.

Keywords:

• Linear model
• Change-point
• Random censoring
• LAD

Acknowledgments

The authors thank referees for their careful reading of the paper and constructive suggestions that greatly improved the paper.

Funding

This work was supported by Zhejiang Provincial Natural Science Foundation of China (No. LY15A010019) and the Natural Science Foundation of China (No. 11501250).