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2021 Simultaneous confidence intervals for ranks using the partitioning principle
Diaa Al Mohamad, Erik van Zwet, Aldo Solari, Jelle Goeman
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Electron. J. Statist. 15(1): 2608-2646 (2021). DOI: 10.1214/21-EJS1847

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 1α. 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.

Funding Statement

This research is supported by VIDI grant number 639.072.412.

Citation

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Diaa Al Mohamad. Erik van Zwet. Aldo Solari. Jelle Goeman. "Simultaneous confidence intervals for ranks using the partitioning principle." Electron. J. Statist. 15 (1) 2608 - 2646, 2021. https://doi.org/10.1214/21-EJS1847

Information

Received: 1 March 2020; Published: 2021
First available in Project Euclid: 6 May 2021

Digital Object Identifier: 10.1214/21-EJS1847

Subjects:
Primary: 62F07
Secondary: 62F03 , 62F30

Keywords: likelihood ratio test , rankings , simple order , Tukey’s HSD

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Vol.15 • No. 1 • 2021
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