  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.
