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“Building” exact confidence nets

Francis, Andrew R., Stehlík, Milan and Wynn, Henry P. ORCID: 0000-0002-6448-1080 (2017) “Building” exact confidence nets. Bernoulli, 23 (4B). pp. 3145-3165. ISSN 1350-7265

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Identification Number: 10.3150/16-BEJ839


Confidence nets, that is, collections of confidence intervals that fill out the parameter space and whose exact parameter coverage can be computed, are familiar in nonparametric statistics. Here, the distributional assumptions are based on invariance under the action of a finite reflection group. Exact confidence nets are exhibited for a single parameter, based on the root system of the group. The main result is a formula for the generating function of the coverage interval probabilities. The proof makes use of the theory of “buildings” and the Chevalley factorization theorem for the length distribution on Cayley graphs of finite reflection groups.

Item Type: Article
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Additional Information: © 2017 International Statistical Institute/Bernoulli Society for Mathematical Statistics and Probability
Divisions: Centre for Analysis of Time Series
Subjects: Q Science > QA Mathematics
Date Deposited: 02 Jun 2017 16:17
Last Modified: 18 Mar 2024 12:24

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