We study the nonasymptotic properties of a general norm penalized estimator, which include Lasso, weighted Lasso, and group Lasso as special cases, for sparse high-dimensional misspecified Cox models with time-dependent covariates. Under suitable conditions on the true regression coefficients and random covariates, we provide oracle inequalities for prediction and estimation error based on the group sparsity of the true coefficient vector. The nonasymptotic oracle inequalities show that the penalized estimator has good sparse approximation of the true model and enables to select a few meaningful structure variables among the set of features.

中文翻译：

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高维指定不正确的Cox模型中加权组套索的Oracle不等式

我们研究稀疏的高维错误指定Cox模型（具有时变协变量）的一般范数惩罚估计量的非渐近性质，其中包括套索，加权套索和组套索。在真实回归系数和随机协变量的适当条件下，我们基于真实系数向量的组稀疏性为预测和估计误差提供预言性不等式。非渐近预言不等式表明，惩罚估计量具有真实模型的良好稀疏近似，并能够在特征集中选择一些有意义的结构变量。