The Annals of Statistics
- Ann. Statist.
- Volume 44, Number 6 (2016), 2564-2593.
Minimax optimal rates of estimation in high dimensional additive models
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal a behavior universal to this class of high dimensional problems. In the sparse regime when the components are sufficiently smooth or the dimensionality is sufficiently large, the optimal rates are identical to those for high dimensional linear regression and, therefore, there is no additional cost to entertain a nonparametric model. Otherwise, in the so-called smooth regime, the rates coincide with the optimal rates for estimating a univariate function and, therefore, they are immune to the “curse of dimensionality.”
Ann. Statist., Volume 44, Number 6 (2016), 2564-2593.
Received: August 2015
Revised: November 2015
First available in Project Euclid: 23 November 2016
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Yuan, Ming; Zhou, Ding-Xuan. Minimax optimal rates of estimation in high dimensional additive models. Ann. Statist. 44 (2016), no. 6, 2564--2593. doi:10.1214/15-AOS1422. https://projecteuclid.org/euclid.aos/1479891628