Determination of Admissible Values of Parameters from the Estimated Accuracy of Data

Abstract

In the traditional parameter estimation approach, confidence intervals for parameters are computed using statistical assumptions, such as the randomness of the sample and a normal distribution of errors. If these statistical assumptions are omitted, we can still estimate values of the model parameters, but the question is whether we can say anything about their confidence limits. We provide an affirmative answer by showing how for a given analytic expression we can determine admissible values of parameters that are compatible with the accuracy of experimental data. An estimate of relative importance of a particular datum for parameter estimation is obtained as a byproduct; it is defined by the number of occasions when this datum determines the extreme admissible values of parameters that are consistent with its accuracy. Use of the method is illustrated by a case study.