On the asymptotic normality and variance estimation of nondifferentiable survey estimators

Survey estimators of population quantities such as distribution functions and quantiles contain nondifferentiable functions of estimated quantities. The theo- retical properties of such estimators are substantially more complicated to de- rive than those of differentiable estimators. In this article, we provide a unified framework for obtaining the asymptotic design-based properties of two common types of nondifferentiable estimators. Estimators of the first type have an ex- plicit expression, while the second is defined only as the solution to estimating equations. We propose both analytical and replication-based design consistent variance estimators that use kernel regression to estimate limits of nondifferen-