Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models
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稀疏超高维加性模型的非参数独立筛选
- 研究问题
- 当边际回归关系可能高度非线性时，如何在稀疏超高维加性模型中筛选变量，并量化降维后保留相关变量的能力？
- 方法与思路
- 作者将相关学习扩展为边际非参数学习，提出 NIS 及相关筛选方法，并用迭代版本 INIS 改善稀疏加性模型拟合。
- 材料陈述的贡献
- 摘要称在技术条件下具有 sure screening 性质并量化降维程度；模拟和实例报告良好表现及相对比较方法的优势。
- 阅读关注点
- 应核对信号强度、模型稀疏性、非参数拟合与筛选阈值条件，并区分保留真变量的保证、误选控制和最终模型恢复。
- 阅读边界
- 材料为 arXiv 0912.2695v2 预印本摘要，不能据此声称已经同行评审或期刊接收，也不能推断刊本变化；具体技术条件与比较数值未提供。
原文摘要
A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonparametric learning. Our nonparametric independence screening is called NIS, a specific member of the sure independence screening. Several closely related variable screening procedures are proposed. Under the nonparametric additive models, it is shown that under some mild technical conditions, the proposed independence screening methods enjoy a sure screening property. The extent to which the dimensionality can be reduced by independence screening is also explicitly quantified. As a methodological extension, an iterative nonparametric independence screening (INIS) is also proposed to enhance the finite sample performance for fitting sparse additive models. The simulation results and a real data analysis demonstrate that the proposed procedure works well with moderate sample size and large dimension and performs better than competing methods.