Simultaneous confidence intervals for ranks using the partitioning principle

Electronic Journal of Statistics, vol. 15

Abstract

We consider the problem of constructing simultaneous confidence intervals (CIs) for the ranks of n means based on their estimates together with the (known) standard errors of those estimates. We present a generic method based on the partitioning principle in which the parameter space is partitioned into disjoint subsets and then each one of them is tested at level α. The resulting CIs have then a simultaneous coverage of 1−α. We show that any procedure which produces simultaneous CIs for ranks can be written as a partitioning procedure. We present a first example where we test the partitions using the likelihood ratio (LR) test. Then, in a second example we show that a recently proposed method for simultaneous CIs for ranks using Tukey’s honest significant difference test has an equivalent procedure based on the partitioning principle. By embedding these two methods inside our generic partitioning procedure, we obtain improved variants. We illustrate the performance of these methods through simulations and real data analysis on hotel ratings. While the novel method that uses the LR test and its variant produce shorter CIs when the number of means is small, the Tukey-based method and its variant produce shorter CIs when the number of means is high.

Authors 4

1. Diaa Al Mohamad Aachen

   Leiden University Medical Center

   Affiliation as printed

   Leiden University Medical Center, Einthovenweg 20. 2333 ZC Leiden, The Nethlerlands

2. Erik W. van Zwet Aachen

   Leiden University Medical Center

   Affiliation as printed

   Leiden University Medical Center, Einthovenweg 20. 2333 ZC Leiden, The Nethlerlands

3. Aldo Solari

   University of Milano-Bicocca

   Affiliation as printed

   University of Milano-Bicocca, 1 Piazza dell’Ateneo Nuovo. 20126 Milano, Italy

4. Jelle J. Goeman Aachen

   Leiden University Medical Center

   Affiliation as printed

   Leiden University Medical Center, Einthovenweg 20. 2333 ZC Leiden, The Nethlerlands