RODEO for Sparse Nonparametric Regression and Quantile Regression with Censored Data

RODEO is a recently developed general strategy for nonparametric estimation based on the regularization of the estimator derivatives with respect to the smoothing parameters. In the original nonparametric regression framework, RODEO results in a simple yet effective new algorithm for simultaneous bandwidth and variable selection with interesting theoretical properties. In this work we focus on a censored regression model in which only the response variable is (right) censored whereas the covariates, although fully observed, are supposed to live in a high dimensional space. In order to recover a sparse representation of both the regression function and the quantile regression function, we adapt RODEO to the present setting starting from the weighted local linear estimator proposed by Cai (2003). We study its theoretical properties and evaluate its performance on both real and simulated data sets.