Is robustness really robust? Robustness from the point of view of statistics and econometrics with an application for multi-objective optimization

Abstract

Has robustness yes or not a single meaning? Therefore, we return to and broaden the original definition of robustness in econometrics: the error term in a linear equation. The enlargement proceeds in two directions: first, a cardinal one considering the distribution of the error term and other random variables; second, a qualitative one based on the degrees of robustness, a nominal scale. In addition, for the enlargement of the definition a distinction is made between the statistical population and the statistical universe. For us the statistical population covers events and opinions, which are present; the statistical universe events and opinions not only present but also possible. Let us say that the meaning given to robustness depends on the context both for the statistical population and for the statistical universe. As an application, robustness is studied for multi-objective optimization, illustrated by an example of sustainable development in Lithuania.