Median regression and the missing information principle

Ian W. McKeague, Sundarraman Subramanian and Yanqing Sun

ABSTRACT

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.  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.