Correction to Censored Regression Quantiles by S. Portnoy, 98 (2003), 1001–1012

Portnoy (2003) presented an approach to the analysis of censored survival data based on a novel computational method for censored regression quantiles. A theorem on asymptotics was given, but in the course of thesis research, the first two authors found a major error in the proof. We have been unable to fix this proof as presented. However, a closely related “grid” algorithm is now our default method, and here we present correct results providing consistency at root-n rate for this grid algorithm. (Details of the proof are rather complicated and have been given in Neocleous 2005 and Vanden Branden 2005.) Portnoy [2003, eqs. (5) and (6)] gave a general model for censored quantile regression, where the regression coefficients are {β(τ)} mapping 0 ≤ τ ≤ 1 to p as a vector of regression coefficients such that x′ iβ(τ ) gives the τ th conditional quantile of the response Yi given the explanatory variables xi . The censoring times and censoring indicators are denoted by {(Ci, i) : i = 1, . . . , n}. The distribution of {(Yi,Ci, i)} remains as given by Portnoy (2003). To define the “grid” algorithm, let > 0 be given and define a grid of τ -values, ≤ t1 < t2 < · · ·< tM ≤ 1 − . In addition, define the parameters along the grid,