Sparse estimation and inference for censored median regression

Justin Hall Shows, Wenbin Lu, Hao Helen Zhang

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Censored median regression has proved useful for analyzing survival data in complicated situations, say, when the variance is heteroscedastic or the data contain outliers. In this paper, we study the sparse estimation for censored median regression models, which is an important problem for high dimensional survival data analysis. In particular, a new procedure is proposed to minimize an inverse-censoring-probability weighted least absolute deviation loss subject to the adaptive LASSO penalty and result in a sparse and robust median estimator. We show that, with a proper choice of the tuning parameter, the procedure can identify the underlying sparse model consistently and has desired large-sample properties including root-n consistency and the asymptotic normality. The procedure also enjoys great advantages in computation, since its entire solution path can be obtained efficiently. Furthermore, we propose a resampling method to estimate the variance of the estimator. The performance of the procedure is illustrated by extensive simulations and two real data applications including one microarray gene expression survival data.

Original languageEnglish (US)
Pages (from-to)1903-1917
Number of pages15
JournalJournal of Statistical Planning and Inference
Issue number7
StatePublished - Jul 2010


  • Censored quantile regression
  • Inverse censoring probability
  • Solution path

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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