How Better Are Predictive Models: Analysis on the Practically Important Example of Robust Interval Uncertainty

Abstract

One of the main applications of science and engineering is to predict future value of different quantities of interest. In the traditional statistical approach, we first use observations to estimate the parameters of an appropriate model, and then use the resulting estimates to make predictions. Recently, a relatively new predictive approach has been actively promoted, the approach where we make predictions directly from observations. It is known that in general, while the predictive approach requires more computations, it leads to more accurate predictions. In this paper, on the practically important example of robust interval uncertainty, we analyze how more accurate is the predictive approach. Our analysis shows that predictive models are indeed much more accurate: asymptotically, they lead to estimates which are \(\sqrt{n}\) more accurate, where n is the number of estimated parameters.