Partially functional linear regression in high dimensions
Partially functional linear regression in high dimensions
复制标题
DOI：
10.1093/biomet/asv062
复制
发表时间：
2016-03-01
期刊：
影响因子：
2.7
通讯作者：
Zhang, Hao H.
中科院分区：
文献类型：
--
作者：
Kong, Dehan;Xue, Kaijie;Zhang, Hao H.
在现代实验中，当观测数据来自随机过程和高维标量协变量时，经常同时遇到函数和非函数数据。现有的模型选择和估计方法难以应用。我们提出了一类新的部分泛函线性模型来刻画标量响应与函数和标量类型的协变量之间的回归。新方法提供了一个统一和灵活的框架，同时考虑了多个泛函和超高维标量预报器，使我们能够识别重要的特征，并提供更好的估计器的可解释性。函数预报器的基本过程被认为是无限维的，我们的贡献之一是表征正则化对结果估计的影响。我们建立了该方法在温和条件下的一致性和Oracle性质，通过仿真研究验证了该方法的性能，并以大气污染数据为例说明了该方法的应用。
In modern experiments, functional and nonfunctional data are often encountered simultaneously when observations are sampled from random processes and high-dimensional scalar covariates. It is difficult to apply existing methods for model selection and estimation. We propose a new class of partially functional linear models to characterize the regression between a scalar response and covariates of both functional and scalar types. The new approach provides a unified and flexible framework that simultaneously takes into account multiple functional and ultrahigh-dimensional scalar predictors, enables us to identify important features, and offers improved interpretability of the estimators. The underlying processes of the functional predictors are considered to be infinite-dimensional, and one of our contributions is to characterize the effects of regularization on the resulting estimators. We establish the consistency and oracle properties of the proposed method under mild conditions, demonstrate its performance with simulation studies, and illustrate its application using air pollution data.