On sharp nonparametric estimation of differentiable functions.

Sharp minimax nonparametric estimation is well known for functions from a Sobolev ellipsoid which is defined via Fourier coefficients of differentiable functions with specific boundary conditions. The theory is based on a renown lower bound of Pinsker (1980) and an adaptive estimator that attains it. This paper solves a long-standing problem of adaptive estimation without assuming boundary conditions. [ABSTRACT FROM AUTHOR]