The Annals of Statistics
- Ann. Statist.
- Volume 29, Number 6 (2001), 1601-1619.
Adaptive Prediction and Estimation in Linear Regression with Infinitely Many Parameters
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.
Ann. Statist., Volume 29, Number 6 (2001), 1601-1619.
First available in Project Euclid: 5 March 2002
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Goldenshluger, A.; Tsybakov, A. Adaptive Prediction and Estimation in Linear Regression with Infinitely Many Parameters. Ann. Statist. 29 (2001), no. 6, 1601--1619. doi:10.1214/aos/1015345956. https://projecteuclid.org/euclid.aos/1015345956