Confidence Intervals for Population Ranks in the Presence of Ties and Near Ties

Frequentist confidence intervals for population ranks and their statistical justifications;ire not well established. even though here is a great need for such procedures in a practice. How do we assign confidence bounds for the ranks of health care facilities, school, and financial institution based on data that do not clearly separate the performance of different entities apart? The commonly used bootstrap-based frequentist confidence intervals and Bayesian intervals for population ranks may not achieve the intended coverage probability ill the frequentist sense, especially in the presence of unknown ties or "near ties" among the population to be ranked. Given random samples from k populations, we propose confidence bounds for population ranking parameters and develop rigorous frequentist theory and nonstandard bootstrap inference for population ranks, which allow ties and near ties. In the process, a notion of modified population rank is introduced that appears quite suitable for dealing with the population ranking problem. The proposed methodology and theoretical results are illustrated through simulations and real dataset from a health research study involving 79 Veteran Health Administration (VHA) facilities. The results tire extended to general risk adjustment models.