Strongly optimal algorithms and optimal information in estimation problems

This paper studies some aspects of information-based complexity theory applied to estimation, identification, and prediction problems. Particular emphasis is given to constructive aspects of optimal algorithms and optimal information, taking into account the characteristics of certain types of problems. Special attention is devoted to the investigation of strongly optimal algorithms and optimal information in the linear case. Two main results are obtained for the class of problems considered. First, central algorithms are proved to be strongly optimal. Second, a simple solution is given to a particular case of optimal information, called optimal sampling design, which is of great interest in system and identification theory.