Open Access
Translator Disclaimer
December 2001 Adaptive Prediction and Estimation in Linear Regression with Infinitely Many Parameters
A. Goldenshluger, A. Tsybakov
Ann. Statist. 29(6): 1601-1619 (December 2001). DOI: 10.1214/aos/1015345956


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.


Download Citation

A. Goldenshluger. A. Tsybakov. "Adaptive Prediction and Estimation in Linear Regression with Infinitely Many Parameters." Ann. Statist. 29 (6) 1601 - 1619, December 2001.


Published: December 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1043.62076
MathSciNet: MR1891740
Digital Object Identifier: 10.1214/aos/1015345956

Primary: 62G05 , 62G20

Keywords: Adaptive prediction , blockwise Stein’s rule , exact asyptotics of minimax risk , Linear regression with infinitely many parameters , Oracle inequalities

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 6 • December 2001
Back to Top