Simultaneous inference for proportions in arbitrary sampling designs

Abstract

In these paper simultaneous confidence intervals for proportions in arbitrary sampling schemes are constructed. To accomplish this the asymptotic joint distribution of proportions is derived in arbitrary sampling designs. An application to household proportions in Germany in 1993 and Monte Carlo simulations are given. It turns out that conventional estimators fail in some sampling designs while the confidence intervals taking into account the sampling design behave well in all instances.