Confidence intervals for population ranks in the presence of ties and near ties

Minge Xie, Kesar Singh, Cun Hui Zhang

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Frequentist confidence intervals for population ranks and their statistical justifications are not well established, even though there is a great need for such procedures in practice. How do we assign confidence bounds for the ranks of health care facilities, schools, and financial institutions 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 in the frequentist sense, especially in the presence of unknown ties or "near ties" among the populations to be ranked. Given random samples from κ 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 a real dataset from a health research study involving 79 Veterans Health Administration (VHA) facilities. The results are extended to general risk adjustment models.

Original languageEnglish (US)
Pages (from-to)775-788
Number of pages14
JournalJournal of the American Statistical Association
Issue number486
StatePublished - Jun 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Large sample theory
  • Nonstandard bootstrap inference
  • Rank inference
  • Slow convergence rate


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