Minimax optimal rates of estimation in high dimensional additive models
高维加性模型估计的极小极大最优收敛率
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…