A general method for local sensitivity analysis with application to regression models and other optimization problems

This article introduces a method for sensitivity analysis of general applicability. The method is based on the well-known duality property of mathematical programming, which states that the partial derivatives of the primal objective function with respect to the constraints on the right side parameters are the negative of the optimal values of the dual problem variables. For the parameters or data, for which sensitivities are sought, to appear on the right side, they are converted into artificial variables and set to their actual values, thus obtaining the desired constraints. The method is applicable to linear and nonlinear models, to normal and nonnormal models, and to least squares and other methods of estimation. In addition to its general applicability, the method is also computationally inexpensive, because the necessary information becomes available without extra calculations. The theoretical basis for the method is given and illustrated by its application to least squares, least absolute value, and minimax regression problems and to the estimation of a Weibull distribution from censored data.