Estimación presuavizada de las funciones de densidad y distribución con datos censurados

Abstract

In survival analysis, right random censored data may arise, that is, individuals whose failure time cannot be registered. The Kaplan-Meier (1958) estimator is the classical estimator of the distribution function in this context. In this work, a new method based on the previous estimation of the conditional probability of uncensoring is presented. This preliminary step, called presmoothing, uses the information in a more efficient way. The asymptotic properties of the presmoothed estimators of the distribution and density functions are studied, together with their efficiency. Besides, an asymptotic representation of the MISE and the bandwidths minimizing it is obtained. A plug-in bandwidth selector is proposed, and its consistency in probability is proved. Its behavior, together with that of other bandwidth selectors based on boostrap resampling are analyzed in a simulation study. The effect of presmoothing when using two different estimators of the condicional probability of uncensoring is studied. In particular, the Nadaraya-Watson and the local linear smoother are compared. Finally, we illustrate the performance of the presmoothed estimators of the distribution and density functions in a real data example.