This kind of result usually is called a Bahadur representation. For the case where [F. Correspondingly, for the case that [F.
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These sharp results involve considerable effort. In this article we give a general result Theorem 1 stating that under regularity conditions on F must be smooth and strictly increasing but does not have to be a distribution function , if 1. From a statistical applications standpoint this is all that is needed, because it is enough to infer a weak convergence result for the quantile process.
The idea in the proof of Theorem 1 is based on a lemma of Vervaat and seems to be known see, Shorack and Wellner , pp. Censored quantile regression with high-dimensional features. Discussion and future directions. Conflict of interest. Quantile regression for survival data in modern cancer research: expanding statistical tools for precision medicine Hyokyoung G Hong.
Oxford Academic. Google Scholar. David C Christiani. Yi Li. Correspondence: Yi Li, yili umich. Cite Citation. Permissions Icon Permissions. Abstract Quantile regression links the whole distribution of an outcome to the covariates of interest and has become an important alternative to commonly used regression models. We begin by introducing the concept of quantiles, followed by censored quantile regression. When the quantile is defined based on the distribution of T alone, without considering covariates, X , it is called the marginal quantile or unconditional quantile.
A quantile regression describes how the covariate or covariate vector of interest impacts the conditional quantiles of the outcome. Figure 1. Open in new tab Download slide. Figure 2.
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Semiparametric analysis of interval-censored survival data with median regression model. Springer, Cham, For commercial re-use, please contact journals. Issue Section:. Download all figures.
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