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Projection‐based and cross‐validated estimation in high‐dimensional Cox model

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  • Haixiang Zhang
  • Jian Huang
  • Liuquan Sun

Abstract

We propose a projection‐based cross‐validation method for estimating a low‐dimensional parameter in the presence of a high‐dimensional nuisance parameter in the Cox regression model. We show that the proposed estimator is asymptotically normal, which enables us to conduct hypothesis test for the parameter of interest with high‐dimensional nuisance parameters. Three decision rules are presented to avoid the influence of random splitting of samples. Simulation studies indicate that our method is more powerful than that of Fang et al. (2017, JRSSB) when the coefficients of predictors are high‐dimensional and not very sparse. As an illustrative example, we apply our procedure to a breast cancer study.

Suggested Citation

  • Haixiang Zhang & Jian Huang & Liuquan Sun, 2022. "Projection‐based and cross‐validated estimation in high‐dimensional Cox model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 353-372, March.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:1:p:353-372
    DOI: 10.1111/sjos.12515
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    References listed on IDEAS

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