Accurate confidence intervals for inter-laboratory calibration and common mean estimation

Abstract For a calibration problem that arises in analytical chemistry, the Rocke-Lorenzato model and some generalizations are considered, so as to capture the near constant variability at very low levels of the analyte, and the increasing measurement variation with increased concentration of the analyte. For the common mean problem, a heteroscedastic one-way random effects model is often used to model the data and will be considered herein. Existing interval estimation procedures for these problems are likelihood based large sample procedures, and are not satisfactory, especially for small samples. A modified likelihood methodology, which can be numerically implemented, is shown to perform very well for the above problems. The analysis of inter-laboratory data is reported in order to illustrate the application of the proposed methods.