Improved Confidence Intervals Based on Combined Information in Univariate Calibration

The problem of testing or estimating a common explanatory variable based on combined information from independent calibration models is addressed. The response variables are measured using different instruments, methods, or at different laboratories. It is assumed that the calibration model at each source is a simple linear regression model and the model parameters at the different sources are different. In this scenario, the problem of constructing a confidence interval (CI) for a common unknown value of the explanatory variable is addressed. CIs for the unknown explanatory variable that can be found by inverting some popular combined tests are proposed. These CIs are exact and better than a CI in the literature. All CIs are compared with respect to precision and some recommendations are made. Interval estimation methods are illustrated using two examples.