Confidence intervals for distributional positions

Journal article, 2024

A common problem with ranking lists (e.g., regarding success/failure proportions of treatments at hospitals) is that smaller units tend to end up either in the top or in the bottom just by pure chance. To alleviate this problem, we propose a method that, for a given unit, gives a confidence interval for the position of this unit within the distribution of the other units. The confidence interval is based on asymptotic normality. The method is illustrated by an empirical example. The small sample confidence level is investigated in a simulation study.