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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 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