Georgia Institute of Technology College of Sciences

Adaptive estimation of linear functionals occupies an important position in the theory of nonparametric function estimation. In this talk I will discuss an adaptation theory for estimation as well as for the construction of confidence intervals for linear functionals. A between class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability and in the construction of adaptive procedures in the same way that the usual modulus of continuity captures the minimax difficulty of estimation over a single parameter space. Our results thus "geometrize" the degree of adaptability.