The dantzig selector for censored linear regression models

Yi Li, Lee Dicker, Sihai Dave Zhao

Research output: Contribution to journalArticlepeer-review

Abstract

The Dantzig variable selector has recently emerged as a powerful tool for fitting regularized regression models. To our knowledge, most work involving the Dantzig selector has been performed with fully-observed response variables. This paper proposes a new class of adaptive Dantzig variable selectors for linear regression models when the response variable is subject to right censoring. This is motivated by a clinical study to identify genes predictive of event-free survival in newly diagnosed multiple myeloma patients. Under some mild conditions, we establish the theoretical properties of our procedures, including consistency in model selection and the optimal efficiency of estimation. The practical utility of the proposed adaptive Dantzig selectors is verified via extensive simulations. We apply our new methods to the aforementioned myeloma clinical trial and identify important predictive genes.

Original languageEnglish (US)
Pages (from-to)251-268
Number of pages18
JournalStatistica Sinica
Volume24
Issue number1
DOIs
StatePublished - Jan 2014
Externally publishedYes

Keywords

  • Buckley-James imputation
  • Censored linear regression
  • Dantzig selector
  • Oracle property

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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