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Adaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates

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  • Guilloux, Agathe
  • Lemler, Sarah
  • Taupin, Marie-Luce

Abstract

We propose a novel kernel estimator of the baseline function in a general high-dimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the regression parameter in the Cox model via a LASSO procedure. We then plug this estimator into the classical kernel estimator of the baseline function, obtained by smoothing the so-called Breslow estimator of the cumulative baseline function. We propose and study an adaptive procedure for selecting the bandwidth, in the spirit of Goldenshluger and Lepski (2011). We state non-asymptotic oracle inequalities for the final estimator, which leads to a reduction in the rate of convergence when the dimension of the covariates grows.

Suggested Citation

  • Guilloux, Agathe & Lemler, Sarah & Taupin, Marie-Luce, 2016. "Adaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 141-159.
    • Handle: RePEc:eee:jmvana:v:148:y:2016:i:c:p:141-159
    DOI: 10.1016/j.jmva.2016.03.002
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    References listed on IDEAS

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    1. Gaëlle Chagny, 2015. "Adaptive Warped Kernel Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 336-360, June.
    2. Lu Tian & Ash A. Alizadeh & Andrew J. Gentles & Robert Tibshirani, 2014. "A Simple Method for Estimating Interactions Between a Treatment and a Large Number of Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1517-1532, December.
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    Cited by:

    1. Honda, Toshio & Yabe, Ryota, 2017. "Variable selection and structure identification for varying coefficient Cox models," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 103-122.

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