Speeding up the asymptotics when constructing one-sided coverage intervals with survey data

Abstract

Coverage intervals for a parameter are frequently derived from a survey sample by assuming that the randomization-based parameter estimate is asymptoti- cally normal and that the associated measure of the estimatorâ??s variance is roughly chi-squared. In many situations, however, the size of the sample and the nature of the parameter being estimated render the conventional Wald technique dubious, es- pecially when a one-sided coverage interval is needed. We will propose a method of coverage-interval construction that â??speeds up the asymptoticsâ?? so that the resulting one-sided intervals can have much better coverage properties than corresponding Wald intervals. For the important case of a mean computed from a stratified, simple ran- dom sample with or without replacement, no model need be assumed. A simulation demonstrates the usefulness of our intervals.