On the solution of an optimal recovery problem and its applications in nonparametric statistics
- Leonov, Sergei
2010 Mathematics Subject Classification
- 62G07 62G20 49J30 90C25
- Asymptotic minimax risk, exact constant, Hölder function class, optimal control, compactness of support, Bahadur efficiency
We consider a non-stochastic optimization problem which arises in various nonparametric statistical settings with Hölder function classes. We prove that the solution of this problem is finite. The application of the finiteness is illustrated via regression estimation with minimax Bahadur risk.