Sparse Estimation and Inference for Censored Median Regression

Censored median regression models have been shown to be useful for analyzing a variety of censored survival data with the robustness property. We study sparse estimation and inference of censored median regression. The new method minimizes an inverse censoring probability weighted least absolute deviation subject to the adaptive LASSO penalty. We show that, with a proper choice of the tuning parameter, the proposed estimator has nice theoretical properties such as root-n consistency and asymptotic normality. The estimator can also identify the underlying sparse model consistently. We propose using a resampling method to estimate the variance of the proposed estimator. Furthermore, the new procedure enjoys great advantages in computation, since its entire solution path can be obtained efficiently. Also, the method can be extended to multivariate survival data, where there is a natural or artificial clustering structure. The performance of our estimator is evaluated by extensive simulations and two real data applications.