Oracle inequalities for weighted group lasso in high-dimensional misspecified Cox models

Abstract

Abstract 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.

Keywords

• Proportional hazard model
• Partial likelihood
• Time-dependent data
• Weighted group Lasso
• Oracle inequalities
• Suprema of empirical processes