Estimation of the Reliability of Parameters Obtained by Non-linear Regression

Abstract

Four methods for estimating the reliability of parameters obtained by non‐linear regression are compared. Matrix inversion demands the least computational effort, but can be unreliable for over‐determined models. The ‘jack‐knife’ technique was found to give results of the right magnitude, but some unexplained discrepancies suggest that this method should be used with caution. A Monte Carlo method and the method of support planes were found to be in good agreement with matrix inversion, but both involve a substantial computational investment. The method of support planes is preferred as it gives information on the degree of non‐linearity of the equation which is fitted to the data.