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SCAD-penalized regression in additive partially linear proportional hazards models with an ultra-high-dimensional linear part

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  • Lian, Heng
  • Li, Jianbo
  • Tang, Xingyu

Abstract

We consider the problem of simultaneous variable selection and estimation in additive partially linear Cox’s proportional hazards models with high-dimensional or ultra-high-dimensional covariates in the linear part. Under the sparse model assumption, we apply the smoothly clipped absolute deviation (SCAD) penalty to select the significant covariates in the linear part and use polynomial splines to estimate the nonparametric additive component functions. The oracle property of the estimator is demonstrated, in the sense that consistency in terms of variable selection can be achieved and that the nonzero coefficients are asymptotically normal with the same asymptotic variance as they would have if the zero coefficients were known a priori. Monte Carlo studies are presented to illustrate the behavior of the estimator using various tuning parameter selectors.

Suggested Citation

  • Lian, Heng & Li, Jianbo & Tang, Xingyu, 2014. "SCAD-penalized regression in additive partially linear proportional hazards models with an ultra-high-dimensional linear part," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 50-64.
    • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:50-64
    DOI: 10.1016/j.jmva.2013.12.002
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    References listed on IDEAS

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    Cited by:

    1. Xiaochao Xia & Binyan Jiang & Jialiang Li & Wenyang Zhang, 2016. "Low-dimensional confounder adjustment and high-dimensional penalized estimation for survival analysis," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 547-569, October.
    2. Arfan Raheen Afzal & Jing Yang & Xuewen Lu, 2021. "Variable selection in partially linear additive hazards model with grouped covariates and a diverging number of parameters," Computational Statistics, Springer, vol. 36(2), pages 829-855, June.

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