The problem of adaptive prediction and estimation in the stochastic linear regression model with infinitely many parameters is considered.We suggest a prediction method that is sharp asymptotically minimax adaptive over ellipsoids in $\ell_2$. The method consists in an application of blockwise Stein’s rule with “weakly” geometrically increasing blocks to the penalized least squares fits of the first $N$ coefficients. To prove the results we develop oracle inequalities for a sequence model with correlated data.
"Adaptive Prediction and Estimation in Linear Regression with Infinitely Many Parameters." Ann. Statist. 29 (6) 1601 - 1619, December 2001. https://doi.org/10.1214/aos/1015345956