Non Asymptotic Minimax Estimation of Functionals with Noisy Observations

Abstract

The minimax estimation of functionals by a finite number of noisy observations is considered. A new way to formalize the problem that enables one to calculate non asymptotic optimal estimates is proposed. The calculations can be turned into and executed as a computer algorithm or carried out analytically under week assumptions on random variables. Some examples are considered.

Keywords:

• Minimax estimation
• Non asymptotic optimal estimates

Mathematics Subject Classification:

• 62C20
• 62G05