标题： Rodeo：稀疏、贪婪的非参数回归 显示英文标题

标题： Rodeo: Sparse, greedy nonparametric regression

摘要： 我们提出了一种贪婪算法，用于同时进行非参数回归中的局部带宽选择和变量选择。该方法从具有大带宽的局部线性估计器开始，并逐步减小关于带宽的估计梯度较大的变量的带宽。这种方法被称为骑手（regularization of derivative expectation operator），通过一系列假设检验来阈值化导数，易于实现。在回归函数和抽样密度满足某些假设的情况下，证明了应用于局部线性平滑的骑手方法能够避免维数灾难，在相关变量数量上实现了接近最优的最小最大收敛率，就如同这些变量事先被隔离一样。 显示英文摘要

摘要： We present a greedy method for simultaneously performing local bandwidth selection and variable selection in nonparametric regression. The method starts with a local linear estimator with large bandwidths, and incrementally decreases the bandwidth of variables for which the gradient of the estimator with respect to bandwidth is large. The method--called rodeo (regularization of derivative expectation operator)--conducts a sequence of hypothesis tests to threshold derivatives, and is easy to implement. Under certain assumptions on the regression function and sampling density, it is shown that the rodeo applied to local linear smoothing avoids the curse of dimensionality, achieving near optimal minimax rates of convergence in the number of relevant variables, as if these variables were isolated in advance.