Adaptive prediction and estimation in linear regression with infinitely many parameters

A. Goldenshluger; A. Tsybakov

doi:10.1214/aos/1015345956

Adaptive prediction and estimation in linear regression with infinitely many parameters

A. Goldenshluger, A. Tsybakov

Department of Statistics

Research output: Contribution to journal › Article › peer-review

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 ℓ₂. 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.

Original language	English
Pages (from-to)	1601-1619
Number of pages	19
Journal	Annals of Statistics
Volume	29
Issue number	6
DOIs	https://doi.org/10.1214/aos/1015345956
State	Published - Dec 2001

Keywords

Adaptive prediction
Blockwise stein's rule
Exact asymptotics of minimax risk
Linear regression with infinitely many parameters
Oracle inequalities

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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AB - 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 ℓ2. 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.

KW - Adaptive prediction

KW - Blockwise stein's rule

KW - Exact asymptotics of minimax risk

KW - Linear regression with infinitely many parameters

KW - Oracle inequalities

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ER -

Adaptive prediction and estimation in linear regression with infinitely many parameters

Abstract

Keywords

ASJC Scopus subject areas

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