Minimax optimal rates of estimation in high dimensional additive models
研究了高维加性模型在近似稀疏假设下的极小化最优收敛速率，发现稀疏时与非参数线性回归速率相同，光滑时与单变量函数估计速率相同，不受维数灾难影响。
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.”