Uncertainty Quantification for High-Dimensional Sparse Nonparametric Additive Models
Uncertainty Quantification for High-Dimensional Sparse Nonparametric Additive Models
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DOI：
10.1080/00401706.2019.1665591
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发表时间：
2017-09
期刊：
影响因子：
2.5
通讯作者：
Qi Gao;Randy C. S. Lai;Thomas C.M. Lee;Yao Li
中科院分区：
文献类型：
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作者：
Qi Gao;Randy C. S. Lai;Thomas C.M. Lee;Yao Li
摘要高维环境下的统计推断最近在文献中引起了极大的关注。然而，大多数已发表的工作集中在参数线性回归问题。本文考虑了这个问题的一个重要扩展：高维稀疏非参数可加模型的统计推断。更准确地说，本文开发了一种在所有候选模型的集合上构造概率密度函数的方法。该方法还可以应用于构造各种感兴趣的量（例如噪声方差）的置信区间和加性函数的置信带。这种方法是使用一个广义的基准推理框架。结果表明，所提出的方法产生的结果享有正确的渐近频率论性质。从数值实验中得到的经验结果验证了这一理论主张。最后，该方法被应用到基因表达数据集，并发现了新的发现，大多数现有的方法的基础上参数线性建模未能观察到。
Abstract Statistical inference in high-dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This article considers an important extension of this problem: statistical inference for high-dimensional sparse nonparametric additive models. To be more precise, this article develops a methodology for constructing a probability density function on the set of all candidate models. This methodology can also be applied to construct confidence intervals for various quantities of interest (such as noise variance) and confidence bands for the additive functions. This methodology is derived using a generalized fiducial inference framework. It is shown that results produced by the proposed methodology enjoy correct asymptotic frequentist properties. Empirical results obtained from numerical experimentation verify this theoretical claim. Lastly, the methodology is applied to a gene expression dataset and discovers new findings for which most existing methods based on parametric linear modeling failed to observe.