Estimation of Absolutely Continuous Distributions for Censored Variables in Two-Sample Nonparametric and Semi-Parametric Models

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, and $n^{1/2}\text{-consistent}$ 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.