CALIBRATION WITH A NONLINEAR STANDARD CURVE - HOW TO DO IT

In this paper, we consider the problem of calibration analysis when the response function is modelised by some nonlinear function of the parameters. Confidence sets based on various statistics are introduced. Using an ad hoc asymptotic framework, we show that these statistics are asymptotically pivotal, admit an Edgeworth expansion and can be bootstrapped in order to obtain confidence sets with second order correct coverage probability. These confidence sets are also compared on the basis of a simulation study. Recommendation for the choice of a calibration procedure are proposed on the basis of both theoretical and empirical results.