Scheffé-type Confidence Region for the Calibration Line

Abstract

Analyzed is the comparative calibration problem in the case when linear relationship is assumed between two considered measuring devices. The method deriving the approximate confidence region for the unknown parameters of the calibration line based on estimation of the calibration line via replicated errors-in-variables model is given inWimmer et al. (2004). Essential point in this approach is the use of the F-approximation of the distribution of the F-statistic suggested by Kenward and Roger (1997). Moreover, in Wimmer and Witkovský (2005) such a calibration procedure is conducted which enables proper interval estimates of several unknown values based on the next independent measurement results obtained by the less precise measuring device. The present contribution is a continuation of work presented in Wimmer et al. (2004) and Wimmer and Witkovský (2005). Derived is the Scheffé-type confidence region for the (whole) calibration line. This enables to construct the interval estimators for the multiple-use calibration case.