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ℓ0-Regularized high-dimensional accelerated failure time model

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  • Cheng, Chao
  • Feng, Xingdong
  • Huang, Jian
  • Jiao, Yuling
  • Zhang, Shuang

Abstract

We develop a constructive approach for ℓ0-penalized estimation in the sparse accelerated failure time (AFT) model with high-dimensional covariates. The proposed approach is based on Stute's weighted least squares criterion combined with ℓ0-penalization. This method is a computational algorithm that generates a sequence of solutions iteratively, based on active sets derived from primal and dual information and root finding according to the Karush-Kuhn-Tucker (KKT) conditions. We refer to the proposed method as AFT-SDAR (for support detection and root finding). An important aspect of our theoretical results is that we directly concern the sequence of solutions generated based on the AFT-SDAR algorithm. We prove that the estimation errors of the solution sequence decay exponentially to the optimal error bound with high probability, as long as the covariate matrix satisfies a mild regularity condition which is necessary and sufficient for model identification even in the setting of high-dimensional linear regression. An adaptive version of AFT-SDAR is also proposed, i.e., AFT-ASDAR, which determines the support size of the estimated coefficient in a data-driven fashion. Simulation studies demonstrate the superior performance of the proposed method over the lasso and MCP in terms of accuracy and speed. The application of the proposed method is also illustrated by analyzing a real data set.

Suggested Citation

  • Cheng, Chao & Feng, Xingdong & Huang, Jian & Jiao, Yuling & Zhang, Shuang, 2022. "ℓ0-Regularized high-dimensional accelerated failure time model," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:csdana:v:170:y:2022:i:c:s016794732200010x
    DOI: 10.1016/j.csda.2022.107430
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    References listed on IDEAS

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