Strong representation of a generalized product-limit estimator for truncated and censored data with some applications

Abstract

An almost sure representation is obtained for a generalized product-limit estimator of the conditional distribution function when the data are subject to random left truncation and right censorship. This result extends strong representations studied on conditional survival analysis for censored data (Gónzalez-Manteiga and Cadarso-Suárez, 1994; Van Keilegom and Veraverbeke, 1995a) as well as for truncated data (LaValley and Akritas, 1994). As consequences of this representation we derive the asymptotic normality of the estimator and the weak convergence of the generalized product-limit process.

Keywords:

• Censored data
• truncated data
• generalized product-limit estimator
• kernel estimator
• almost sure representation
• asymptotic normality
• weak convergence

AMS (1991):

• 62607