Univariate Calibration

This article deals with the univariate calibration problem where calibration data come from several independent sources. Such a situation arises when measurements are made using different instruments or methods, or at diierent laboratories. It is assumed that the response variable at each source is normally distributed and the relationship between the response variable and the explanatory variable is a linear regression model, where the model parameters are diierent at the diierent sources. The problem of interest is the construction of a conndence region for a common unknown value of the explanatory variable after observing the corresponding response at each source. The conndence region that is constructed is a multiple use conndence region, i.e., the calibration data will be used repeatedly to construct a sequence of conndence regions for a sequence of unknown values of the explanatory variable. After deriving such a conndence region, its computation is described in detail and illustrated using an example where the data came from two diierent sources. For the example, the conndence regions based on combined information turned out to be narrower than those based on the data from any individual source.