Application of the bootstrap to calibration experiments

In calibration experiments, a number of samples of known concentration are used to establish the relationship between a measured response and sample concentration; this relationship is then used to estimate the unknown concentration of further samples from their measured responses. In addition to the estimates themselves, it is useful to have available some measure of their precision, usually given in the form of confidence limits. The standard method of inverting prediction limits is found to work well in simple situations, but in nonlinear multivariate calibration it becomes intractable. The bootstrap offers an alternative methodology, but in the calibration framework its application is not obvious. We describe some considerations in bootstrapping calibration data and compare our methods with a previous attempt and with the standard method in linear, nonlinear, and multivariate situations. The bootstrap is found to be a useful tool in those situations where the standard method is difficult to implement.