Robust Inference for Censored Quantile Regression

In various fields such as medical science and finance, it is not uncommon that the data are heavy-tailed and/or not fully observed, calling for robust inference methods that can deal with the outliers and incompleteness efficiently. In this paper, the authors propose a rank score test for quantile regression with fixed censored responses, based on the standard quantile regression in an informative subset which is computationally efficient and robust. The authors further select the informative subset by the multiply robust propensity scores, and then derive the asymptotic properties of the proposed test statistic under both the null and local alternatives. Moreover, the authors conduct extensive simulations to verify the validity of the proposed test, and apply it to a human immunodeficiency virus data set to identify the important predictors for the conditional quantiles of the censored viral load.