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Confidence Sets for Ratios: A Purely Geometric Approach To Fieller's Theorem

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons76237

von Luxburg,  U
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84990

Franz,  VH
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

von Luxburg, U., & Franz, V.(2004). Confidence Sets for Ratios: A Purely Geometric Approach To Fieller's Theorem (133).


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-F351-5
Abstract
We present a simple, geometric method to construct Fieller's exact confidence sets for ratios of jointly normally distributed random variables. Contrary to previous geometric approaches in the literature, our method is valid in the general case where both sample mean and covariance are unknown. Moreover, not only the construction but also its proof are purely geometric and elementary, thus giving intuition into the nature of the confidence sets.