A Geometric Comparison of the Delta and Fieller Confidence Intervals

The comparison of the Delta and Fieller confidence intervals for the ratio of parameters estimated by normally distributed random variables has long been of interest. Our contribution is the construction of a common geometric representation of both the Delta and Fieller intervals defined by two related constrained extrema problems that are subject to a common constraint. The diagrammatic solution to these problems can be used to examine how earlier comparisons based on alternate analytic relationships and simulations have resulted in the particular conclusions they report. We find that the degree to which the Delta and Fieller intervals coincide depends not only on the univariate statistics for the estimated parameters, but also on the agreement of the sign of their estimated correlation and the ratio of estimated parameters. This article has supplementary material online.