Median regression and the missing information principle

Median regression analysis has robustness properties which make it an attractive alternative to regression based on the mean. In this paper, the missing information principle is applied to a right-censored version of the median regression model, leading to a new estimator for the regression parameters. Our approach adapts Efron's derivation of self-consistency for the Kaplan-Meier estimator to the context of median regression; we replace the least absolute deviation estimating function by its (estimated) conditional expectation given the data. For discrete covariates the new estimator is shown to be asymptotically equivalent to an ad hoc estimator introduced by Ying, Jung and Wei, and to have improved moderate-sample performance in simulation studies.