Adaptive Prediction and Estimation in Linear Regression with Infinitely Many Parameters
The Annals of Statistics · 2001 · Volume 29 · Issue 6
Abstract
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.
Keywords
62G05, 62G20, Adaptive prediction, blockwise Stein’s rule, exact asyptotics of minimax risk, Linear regression with infinitely many parameters, Oracle inequalities
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