Wimbush, Alexander, Gray, Nicholas 
ORCID: 0000-0002-0930-4575 and Ferson, Scott ORCID: 0000-0002-2613-0650
(2022)
Singhing with confidence: visualising the performance of confidence procedures.
Journal of Statistical Computation and Simulation, 92 (13).
pp. 1-17.
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Abstract
Confidence intervals are an established means of portraying uncertainty about an inferred parameter and can be generated through the use of confidence distributions. For a confidence distribution to be valid, it must maintain frequentist coverage of the true parameter. This can be represented for a precise distribution by adherence to a cumulative unit uniform distribution, a comparison that is referred to here as a Singh plot. This article extends this to imprecise confidence procedures with bounds around the uniform distribution, and describes how deviations convey information regarding the characteristics of confidence procedures designed for inference and prediction. An example of how Singh plots can highlight deficiencies in proposed methods is given with the ProUCL Chebyshev upper confidence limit estimator for the mean of an unknown distribution. Singh plots can quickly inform the appropriate use of procedures such as these and aid the development of novel confidence procedures to avoid similar errors.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Confidence, coverage, imprecise, inference, prediction |
| Divisions: | Faculty of Science and Engineering > School of Engineering |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 04 Apr 2022 15:25 |
| Last Modified: | 18 Jan 2023 21:05 |
| DOI: | 10.1080/00949655.2022.2044814 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3152084 |
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