Variance Estimation in Censored Quantile Regression via Induced Smoothing.

Statistical inference in censored quantile regression is challenging, partly due to the unsmoothness of the quantile score function. A new procedure is developed to estimate the variance of Bang and Tsiatis's inverse-censoring-probability weighted estimator for censored quantile regression by employing the idea of induced smoothing. The proposed variance estimator is shown to be asymptotically consistent. In addition, numerical study suggests that the proposed procedure performs well in finite samples, and it is computationally more efficient than the commonly used bootstrap method.