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Oracle inequalities for the Lasso in the additive hazards model with interval-censored data

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  • Yanqin Feng
  • Yurong Chen

Abstract

This article studies the absolute penalized convex function estimator in sparse and high-dimensional additive hazards model. Under such model, we assume that the failure time data are interval-censored and the number of time-dependent covariates can be larger than the sample size. We establish oracle inequalities based on some natural extensions of the compatibility and cone invertibility factors of the Hessian matrix at the true parameters in the model. Some similar inequalities based on an extension of the restricted eigenvalue are also established. Under mild conditions, we prove that the compatibility and cone invertibility factors and the restricted eigenvalues are bounded from below by positive constants for time-dependent covariates.

Suggested Citation

  • Yanqin Feng & Yurong Chen, 2018. "Oracle inequalities for the Lasso in the additive hazards model with interval-censored data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(12), pages 2927-2949, June.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:12:p:2927-2949
    DOI: 10.1080/03610926.2017.1343850
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