Sparse estimation and inference for censored median regression

Justin Hall Shows, Wenbin Lu, Hao Zhang

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

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
Volume140
Issue number7
DOIs
StatePublished - Jul 2010
Externally publishedYes

Fingerprint

Median Regression
Censored Regression
Survival Data
Microarrays
Gene expression
Tuning
Adaptive Lasso
Least Absolute Deviation
Estimator
Resampling Methods
Entire Solution
Parameter Tuning
High-dimensional Data
Censoring
Gene Expression Data
Asymptotic Normality
Microarray
Outlier
Penalty
Regression Model

Keywords

  • Censored quantile regression
  • Inverse censoring probability
  • LASSO
  • Solution path

ASJC Scopus subject areas

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

Cite this

Sparse estimation and inference for censored median regression. / Shows, Justin Hall; Lu, Wenbin; Zhang, Hao.

In: Journal of Statistical Planning and Inference, Vol. 140, No. 7, 07.2010, p. 1903-1917.

Research output: Contribution to journalArticle

Shows, Justin Hall ; Lu, Wenbin ; Zhang, Hao. / Sparse estimation and inference for censored median regression. In: Journal of Statistical Planning and Inference. 2010 ; Vol. 140, No. 7. pp. 1903-1917.
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