Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models
Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models
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DOI：
10.1080/01621459.2013.879828
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发表时间：
2014-07-03
影响因子：
3.7
通讯作者：
Dai, Wei
中科院分区：
文献类型：
--
作者：
Fan, Jianqing;Ma, Yunbei;Dai, Wei
不同系数模型是一类重要的非参数统计模型，它使我们能够检查协变量的影响如何随曝光变量而变化。当协变量数量很大时，会出现可变选择的问题。在本文中，我们提出并研究了边缘非参数筛选方法，以筛选稀疏超高维不同系数模型中的变量。提出的非参数独立性筛选（NIS）通过对曝光变量进行对每个协变量的非参数边缘贡献的量度进行排名，从而选择变量。当尺寸是非多层秩序并量化NIS的尺寸降低时，确定独立的筛选特性是在某个轻度技术条件下建立的。为了增强实用性和有限样本性能，提出了两个数据驱动的迭代NIS（INIS）方法，以选择阈值参数和变量：条件置换和贪婪的方法，导致条件性Inis和贪婪的Inis。通过模拟研究和实际数据应用进一步说明了所提出方法的有效性和灵活性。
The varying coefficient model is an important class of nonparametric statistical model, which allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is large, the issue of variable selection arises. In this article, we propose and investigate marginal nonparametric screening methods to screen variables in sparse ultra-high-dimensional varying coefficient models. The proposed nonparametric independence screening (NIS) selects variables by ranking a measure of the nonparametric marginal contributions of each covariate given the exposure variable. The sure independent screening property is established under some mild technical conditions when the dimensionality is of nonpolynomial order, and the dimensionality reduction of NIS is quantified. To enhance the practical utility and finite sample performance, two data-driven iterative NIS (INIS) methods are proposed for selecting thresholding parameters and variables: conditional permutation and greedy methods, resulting in conditional-INIS and greedy-INIS. The effectiveness and flexibility of the proposed methods are further illustrated by simulation studies and real data applications.