A nonparametric model-based estimator for the cumulative distribution function of a right censored variable in a finite population

Résumé

In survey analysis, the estimation of the cumulative distribution function (cdf) is of great interest: it allows for instance to derive quantiles estimators or other non linear parameters derived from the cdf. We consider the case where the response variable is a right censored duration variable. In this framework, the classical estimator of the cdf is the Kaplan-Meier estimator. As an alternative, we propose a nonparametric model-based estimator of the cdf in a finite population. The new estimator uses auxiliary information brought by a continuous covariate and is based on nonparametric median regression adapted to the censored case. The bias and variance of the prediction error of the estimator are estimated by a bootstrap procedure adapted to censoring. The new estimator is compared by model-based simulations to the Kaplan-Meier estimator computedwith the sampled individuals: a significant gain in precision is brought by the new method whatever the size of the sample and the censoring rate. Welfare duration data are used to illustrate the new methodology.

Mots-clés

Cumulative distribution function; auxiliary information; censored data; generalized Kaplan-Meier estimator; nonparametric conditional median; bootstrap estimation;