Abstract: 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, confidence intervals, however, have low converge probabilities. An alternative bootstrapping technique is proposed here for Fieller's problems. This produces parametric and nonparametric confidence intervals that closely mimic Fieller's intervals and have good converge probabilities for the normal model and many other parametric models. Also the nonparametric confidence intervals are demonstrated to be second order correct whereas the Fieller's intervals are only first order correct for the nonnormal observations.
Key words and phrases: Bootstrap, nonparametric confidence interval, coverage probability.