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.
Publié le : 2001-12-14
Classification:
Linear regression with infinitely many parameters,
adaptive prediction,
exact asyptotics of minimax risk,
blockwise Stein’s rule,
oracle inequalities,
62G05,
62G20
@article{1015345956,
author = {Goldenshluger, A. and Tsybakov, A.},
title = {Adaptive Prediction and Estimation in Linear Regression with
Infinitely Many Parameters},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 1601-1619},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345956}
}
Goldenshluger, A.; Tsybakov, A. Adaptive Prediction and Estimation in Linear Regression with
Infinitely Many Parameters. Ann. Statist., Tome 29 (2001) no. 2, pp. 1601-1619. http://gdmltest.u-ga.fr/item/1015345956/