Simultaneous confidence sets for ranks using the partitioning principle - Technical report (1708.02729v1)

Abstract: Ranking institutions such as medical centers or universities is based on an indicator accompanied with an uncertainty measure such as a standard deviation, and confidence intervals should be calculated to assess the quality of these ranks. We consider the problem of constructing simultaneous confidence intervals for the ranks of centers based on an observed sample. We present in this paper a novel method based on multiple testing which uses the partitioning principle and employs the likelihood ratio (LR) test on the partitions. The complexity of the algorithm is super exponential. We present several ways and shortcuts to reduce this complexity. We provide also a polynomial algorithm which produces a very good bracketing for the multiple testing by linearizing the critical value of the LR test. We show that Tukey's Honest Significant Difference (HSD) test can be written as a partitioning procedure. The new methodology has promising properties in the sens that it opens the door in a simple and easy way to construct new methods which may trade the exponential complexity with power of the test or vice versa. In comparison to Tukey's HSD test, the LR test seems to give better results when the centers are close to each others or the uncertainty in the data is high which is confirmed during a simulation study.