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  A Geometric Approach to Confidence Sets for Ratios: Fieller‘s Theorem, Generalizations, and Bootstrap

von Luxburg, U., & Franz, V. (2009). A Geometric Approach to Confidence Sets for Ratios: Fieller‘s Theorem, Generalizations, and Bootstrap. Statistica Sinica, 19(3), 1095-1117.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-C3D9-7 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-BE58-6
Genre: Journal Article

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 Creators:
von Luxburg, U1, 2, Author              
Franz, VH1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497794              

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 Abstract: We present a geometric method to determine confidence sets for the ratio E(Y)/E(X) of the means of random variables X and Y. This method reduces the problem of constructing confidence sets for the ratio of two random variables to the problem of constructing confidence sets for the means of one-dimensional random variables. It is valid in a large variety of circumstances. In the case of normally distributed random variables, the so constructed confidence sets coincide with the standard Fieller confidence sets. Generalizations of our construction lead to definitions of exact and conservative confidence sets for very general classes of distributions, provided the joint expectation of (X,Y) exists and the linear combinations of the form aX + bY are well-behaved. Finally, our geometric method allows to derive a very simple bootstrap approach for constructing conservative confidence sets for ratios which perform favorably in certain situations, in particular in the asymmetric heavy-tailed regime.

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 Dates: 2009-07
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: -
 Identifiers: BibTex Citekey: 5080
 Degree: -

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Title: Statistica Sinica
Source Genre: Journal
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Publ. Info: Taipei : Institute of Statistical Science, Academia Sinica; International Chinese Statistical Association
Pages: - Volume / Issue: 19 (3) Sequence Number: - Start / End Page: 1095 - 1117 Identifier: ISSN: 1996-8507
CoNE: https://pure.mpg.de/cone/journals/resource/19968507