Empirical Inference Technical Report 2004

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

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
Bibtex Type: Technical Report (techreport)
Electronic Archiving: grant_archive
Institution: Max Planck Institute for Biological Cybernetics
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik
Links:

BibTex

@techreport{3172,
  title = {Confidence Sets for Ratios: A Purely Geometric Approach To Fieller's Theorem},
  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.},
  number = {133},
  organization = {Max-Planck-Gesellschaft},
  institution = {Max Planck Institute for Biological Cybernetics},
  school = {Biologische Kybernetik},
  year = {2004},
  slug = {3172},
  author = {von Luxburg, U. and Franz, VH.}
}