Abstract
It has been difficult to generalise Kaplan–Meier approaches to censored regression data under the minimal condition that censoring and response are conditionally independent given the explanatory variables. Portnoy [S. Portnoy, Censored regression quantiles, J. Am. Stat. Assoc. 98 (2003), pp. 1001–1012.] provided such a generalisation based on the paradigm of censored quantile regression. However, previous research has only provided consistency results for this approach. The results here provide an asymptotic distribution theory under relatively mild conditions for a gridded version of the algorithm in Portnoy [S. Portnoy, Censored regression quantiles, J. Am. Stat. Assoc. 98 (2003), pp. 1001–1012.], and show that the asymptotics for censored regression quantiles are an exact generalisation of those for the Kaplan–Meier estimator in one sample.
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