VARIABLE SELECTION AND ESTIMATION IN HIGH-DIMENSIONAL VARYING-COEFFICIENT MODELS.
VARIABLE SELECTION AND ESTIMATION IN HIGH-DIMENSIONAL VARYING-COEFFICIENT MODELS.
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DOI：
10.5705/ss.2009.316
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发表时间：
2011-10-01
影响因子：
1.4
通讯作者：
Li H
中科院分区：
文献类型：
--
作者：
Wei F;Huang J;Li H
非参数变系数模型对于研究变量随时间的影响非常有用。已经开发了许多用于此类模型中的估计和变量选择的程序。然而，现有的工作主要集中在变量数量固定或小于样本量的情况。在本文中，我们考虑当变量数量大于样本大小时，稀疏、高维设置中不同系数模型中的变量选择和估计问题。我们应用群套索和基函数展开来同时选择重要变量并估计非零变系数函数。在适当的条件下，我们表明Lasso群选择了正确维数顺序的模型，选择了相应系数函数的范数大于一定阈值水平的所有变量，并且估计是一致的。然而，Lasso 组通常不是选择一致的，并且倾向于选择模型中不重要的变量。为了改善选择结果，我们应用自适应组Lasso。我们证明，在适当的条件下，自适应群 Lasso 具有预言机选择属性，即它正确选择概率收敛于 1 的重要变量。相比之下，Lasso 组不具备这种预言机属性。这两种方法都通过仿真进行评估并通过数据示例进行演示。
Nonparametric varying coefficient models are useful for studying the time-dependent effects of variables. Many procedures have been developed for estimation and variable selection in such models. However, existing work has focused on the case when the number of variables is fixed or smaller than the sample size. In this paper, we consider the problem of variable selection and estimation in varying coefficient models in sparse, high-dimensional settings when the number of variables can be larger than the sample size. We apply the group Lasso and basis function expansion to simultaneously select the important variables and estimate the nonzero varying coefficient functions. Under appropriate conditions, we show that the group Lasso selects a model of the right order of dimensionality, selects all variables with the norms of the corresponding coefficient functions greater than certain threshold level, and is estimation consistent. However, the group Lasso is in general not selection consistent and tends to select variables that are not important in the model. In order to improve the selection results, we apply the adaptive group Lasso. We show that, under suitable conditions, the adaptive group Lasso has the oracle selection property in the sense that it correctly selects important variables with probability converging to one. In contrast, the group Lasso does not possess such oracle property. Both approaches are evaluated using simulation and demonstrated on a data example.
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