Abstract
We consider lifetime data with covariables which are subject to both left truncation and right censorship. In this context, it is interesting to study the conditional distribution function of the lifetime and the corresponding conditional quantile function. A generalized product-limit estimator (GPLE) of the conditional distribution function has been studied in Iglesias-Pérez and González-Manteiga (J. Nonparametric Statist. 10 (1999) 213). In the present paper, we define a conditional quantile function estimator via the mentioned GPLE and we derive an almost sure representation for this quantile estimator. This result extends strong quantile representations studied on conditional survival analysis for censored data (Dabrowska (Sankhya Ser. A 54 (1992) 252) and Van Keilegom and Veraverbeke (J. Statist. Plann. Inference 69 (1998) 115)). As consequence of this representation we establish the asymptotic normality of the conditional quantile estimator.
Published Version
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