Presmoothed Estimation with Left-Truncated and Right-Censored Data

Abstract

We propose a new method to estimate the cumulative hazard function and the corresponding distribution function of survival times under randomly left-truncated and right-censored observations (LTRC). The new estimators are based on presmoothing ideas, the estimation of the conditional expectation m of the censoring indicator. An almost sure representation for both estimators is established, from which a strong consistency rate and asymptotic normality are derived. It is shown that the presmoothed modification leads to a gain in terms of asymptotic mean squared error. This efficiency with respect to the classical estimators is also shown in a simulation study. Finally, an application to a real data set is provided.

Keywords:

• Almost sure representation
• Cumulative hazard function
• Kaplan–Meier estimator
• Presmoothing
• Survival analysis

Mathematics Subject Classification:

• Primary 62G07
• Secondary 62N01