FIELLER ' S PROBLEMS AND RESAMPLING TECHNIQUES

Fieller's problems occur in many areas such as Bioassy and Calibration. The classical solutions based on normality assumptions were proposed in Bliss (1935) and Fieller (1954) and are compared in this paper to the more modern solutions. Based on resampling techniques, con dence intervals have been constructed without the normality assumption. These con dence intervals, however, have low coverage probabilities. An alternative bootstrapping technique is proposed here for Fieller's problems. This produces parametric and nonparametric con dence intervals that closely mimic Fieller's intervals and have good coverage probabilities for the normal model and many other parametric models. Also the nonparametric con dence intervals are demonstrated to be second order correct whereas the Fieller's intervals are only rst order correct for the nonnormal observations.