Optimal algorithms theory for robust estimation and prediction

This paper deals with the theory of optimal algorithms for problems which cannot be solved exactly. The theory developed allows for the derivation of new and interesting results in parameter estimation and in time series prediction in situations where no reliable statistical hypothesis can be made on the functions and modeling errors involved, but only a bound on them is known, in particular, the derivation of computationally simple optimal algorithms for these two problems is investigated. The practical effectiveness of the algorithms obtained is illustrated by several numerical examples.