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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 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 a real dataset from a health research study involving 79 Veterans Health Administration (VHA) facilities. The results are extended to general risk adjustment models. [ABSTRACT FROM AUTHOR]

Intervalles de confiance à rétrécisseur pour l'espérance d'une loi normale: utilisation d'une valeur initiale au profit d'une meilleure efficacité Si l'espérance inconnue d'une population univariée est assez proche d'une valeur initiale, l'erreur quadratique moyenne d'un bon estimateur à rétrécisseur sera plus faible que celle de la moyenne échantillonnale. Ce principe est connu depuis longtemps, mais il ne semble pas avoir été appliqué à l'estimation par intervalle. L'auteur présente des intervalles de confiance 'à rétrécisseur' bilatéraux à 95% et 99% pour l'espérance d'une loi normale. Ces intervalles sont plus courts que l'intervalle habituel fondé sur la loi de Student dès que l'espérance de la population se situe dans un 'intervalle effectif.' On peut observer une réduction de 20% de la longueur moyenne de l'intervalle quand l'espérance de la population est assez proche de la valeur initiale. L'auteur montre aussi comment certains estimateurs ponctuels à rétrécisseur d'une espérance univariée quelconque peuvent être modifiés de façon à élargir l'intervalle effectif. [ABSTRACT FROM AUTHOR]

A capture-recapture model that depends on the "catchability" of the individuals in a closed population is considered. A test is derived to decide if the capture efficiencies are the same for two capture attempts. The test given assumes no a priori information about the population and can be used even if one is dealing with relatively small populations. Statistical inferences are drawn about the size of the population. In particular, a family of point estimators for the population size, N, is investigated and compared with the maximum likelihood estimator. Further, confidence intervals for the capture efficiency, is an element of, are combined with joint confidence regions for N and is an element of to obtain confidence intervals for N. It is found that this procedure yields confidence intervals for N whose actual confidence levels are not strongly dependent on the nuisance parameter is an element of. For N less than or equal to 200 the procedure given for finding confidence intervals for N is found to be more satisfactory than the standard approach of simply replacing is an element of with its maximum-likelihood estimate. [ABSTRACT FROM AUTHOR]