Estimation of absolutely continuous distributions for censored variables in two-sample nonparametric and semi-parametric models

Abstract

This paper considers the estimation of the density of an absolutely continuous distribution with respect to an unknown baseline distribution $F$, and the estimation of $F$, from censored observations. For parametric and nonparametric densities, an $n^{1/2}$-consistent estimator of $F$ is defined from the two samples and the asymptotic distribution of the estimators is studied. The efficient score functions and the minimal variances of the estimators are established.