Precise asymptotic descriptions of the minimax affine risks and bias-variance tradeoffs for estimating linear functionals are given for a broad class of moduli. The results are complemented by illustrative examples including one where it is possible to construct an estimator which is fully adaptive over a range of parameter spaces.
"A note on nonparametric estimation of linear functionals." Ann. Statist. 31 (4) 1140 - 1153, August 2003. https://doi.org/10.1214/aos/1059655908