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


Technical Report


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.

Author(s): von Luxburg, U. and Franz, VH.
Number (issue): 133
Year: 2004
Day: 0

Department(s): Empirical Inference
Bibtex Type: Technical Report (techreport)

Institution: Max Planck Institute for Biological Cybernetics

Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Confidence Sets for Ratios: A Purely Geometric Approach To Fieller's Theorem},
  author = {von Luxburg, U. and Franz, VH.},
  number = {133},
  organization = {Max-Planck-Gesellschaft},
  institution = {Max Planck Institute for Biological Cybernetics},
  school = {Biologische Kybernetik},
  year = {2004}