@article{5080,
  title = {A Geometric Approach to Confidence Sets for Ratios: Fieller's Theorem, Generalizations, and Bootstrap},
  journal = {Statistica Sinica},
  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.},
  volume = {19},
  number = {3},
  pages = {1095-1117},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = jul,
  year = {2009},
  slug = {5080},
  author = {von Luxburg, U. and Franz, VH.},
  month_numeric = {7}
}