Using Nonparametric Conditional M-Quantiles to Estimate a Cumulative Distribution Function in a Domain

Estimating the cumulative distribution function in survey sampling is of interest on the population but also on a sub-population (domain). However, in most practical applications, sample sizes in the domains are not large enough to produce sufficiently precise estimators. Therefore, we propose new nonparametric estimators of the cumulative distribution function in a domain based on M-quantile estimation. The obtained estimators are compared by simulations and applied to real data.