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April 2015 Minimax-optimal nonparametric regression in high dimensions
Yun Yang, Surya T. Tokdar
Ann. Statist. 43(2): 652-674 (April 2015). DOI: 10.1214/14-AOS1289


Minimax $L_{2}$ risks for high-dimensional nonparametric regression are derived under two sparsity assumptions: (1) the true regression surface is a sparse function that depends only on $d=O(\log n)$ important predictors among a list of $p$ predictors, with $\log p=o(n)$; (2) the true regression surface depends on $O(n)$ predictors but is an additive function where each additive component is sparse but may contain two or more interacting predictors and may have a smoothness level different from other components. For either modeling assumption, a practicable extension of the widely used Bayesian Gaussian process regression method is shown to adaptively attain the optimal minimax rate (up to $\log n$ terms) asymptotically as both $n,p\to\infty$ with $\log p=o(n)$.


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Yun Yang. Surya T. Tokdar. "Minimax-optimal nonparametric regression in high dimensions." Ann. Statist. 43 (2) 652 - 674, April 2015.


Published: April 2015
First available in Project Euclid: 3 March 2015

zbMATH: 1312.62052
MathSciNet: MR3319139
Digital Object Identifier: 10.1214/14-AOS1289

Primary: 62C20 , 62G08
Secondary: 60G15

Keywords: adaptive estimation , high-dimensional regression , minimax risk , Model selection , Nonparametric regression

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 2 • April 2015
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