Censored broken adaptive ridge regression in high-dimension

Abstract

Broken adaptive ridge (BAR) is a penalized regression method that performs variable selection via a computationally scalable surrogate to \(L_0\) regularization. The BAR regression has many appealing features; it converges to selection with \(L_0\) penalties as a result of reweighting \(L_2\) penalties, and satisfies the oracle property with grouping effect for highly correlated covariates. In this paper, we investigate the BAR procedure for variable selection in a semiparametric accelerated failure time model with complex high-dimensional censored data. Coupled with Buckley-James-type responses, BAR-based variable selection procedures can be performed when event times are censored in complex ways, such as right-censored, left-censored, or double-censored. Our approach utilizes a two-stage cyclic coordinate descent algorithm to minimize the objective function by iteratively estimating the pseudo survival response and regression coefficients along the direction of coordinates. Under some weak regularity conditions, we establish both the oracle property and the grouping effect of the proposed BAR estimator. Numerical studies are conducted to investigate the finite-sample performance of the proposed algorithm and an application to real data is provided as a data example.