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We present a geometric method to determine confidence sets for the ratioE(Y)/E(X) of the means of random variables X and Y. This method reduces theproblem of constructing confidence sets for the ratio of two random variablesto the problem of constructing confidence sets for the means of one-dimensionalrandom variables. It is valid in a large variety of circumstances. In the caseof normally distributed random variables, the so constructed confidence setscoincide with the standard Fieller confidence sets. Generalizations of ourconstruction lead to definitions of exact and conservative confidence sets forvery 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 approachfor constructing conservative confidence sets for ratios which performfavorably in certain situations, in particular in the asymmetric heavy-tailedregime.

A Geometric Approach to Confidence Sets for Ratios: Fieller's Theorem, Generalizations, and Bootstrap