Nonparametric Model-Based Estimators for the Cumulative Distribution Function of a Right Censored Variable in a Small Area

In survey analysis, the estimation of the cumulative distribution function (cdf) is of great interest as it facilitates the derivation of mean/median estimators for both populations and sub-populations (i.e. domains). We focus on small domains and consider the case where the response variable is right censored. Under this framework, we propose a nonparametric model-based estimator that extends the cdf estimator of Casanova (2012) to the censored case: it uses auxiliary information in the form of a continuous covariate and utilizes nonparametric quantile regression. We then employ simulations to compare the constructed estimator with the model-based cdf estimator of Casanova and Leconte (2015) and the Kaplan–Meier estimator (Kaplan and Meier 1958), both of which use only information contained within the domain: the quantile-based estimator performs better than the former two for very small domain sample sizes. Access times to the first job for young female graduates in the Occitania region are used to illustrate the new methodology.