论文标题
稀疏高维添加剂模型的估计和均匀推断
Estimation and Uniform Inference in Sparse High-Dimensional Additive Models
论文作者
论文摘要
我们开发了一种新颖的方法，用于在稀疏加性模型中为非参数组件$ f_1 $构建有效的置信带$ y = f_1（x_1） + \ ldots + \ ldots + f_p（x_p） + \ varepsilon $在高维设置中。我们的方法将筛估计整合到高维Z估计框架中，从而促进了目标组件$ f_1 $的统一有效置信带的构建。为了形成这些置信带，我们采用了乘数引导程序。此外，我们为高维度的均匀拉索估计提供了率，这可能具有独立的关注。通过仿真研究，我们证明了我们提出的方法在估计和覆盖范围方面也可以提供可靠的结果，即使在小样本中。
We develop a novel method to construct uniformly valid confidence bands for a nonparametric component $f_1$ in the sparse additive model $Y=f_1(X_1)+\ldots + f_p(X_p) + \varepsilon$ in a high-dimensional setting. Our method integrates sieve estimation into a high-dimensional Z-estimation framework, facilitating the construction of uniformly valid confidence bands for the target component $f_1$. To form these confidence bands, we employ a multiplier bootstrap procedure. Additionally, we provide rates for the uniform lasso estimation in high dimensions, which may be of independent interest. Through simulation studies, we demonstrate that our proposed method delivers reliable results in terms of estimation and coverage, even in small samples.
