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November 2017 “Building” exact confidence nets
Andrew R. Francis, Milan Stehlík, Henry P. Wynn
Bernoulli 23(4B): 3145-3165 (November 2017). DOI: 10.3150/16-BEJ839

Abstract

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.

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Andrew R. Francis. Milan Stehlík. Henry P. Wynn. "“Building” exact confidence nets." Bernoulli 23 (4B) 3145 - 3165, November 2017. https://doi.org/10.3150/16-BEJ839

Information

Received: 1 October 2015; Revised: 1 March 2016; Published: November 2017
First available in Project Euclid: 23 May 2017

zbMATH: 06778281
MathSciNet: MR3654801
Digital Object Identifier: 10.3150/16-BEJ839

Keywords: buildings , confidence intervals , confidence nets , Coxeter groups , nonparametrics

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

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Vol.23 • No. 4B • November 2017
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