High dimensional ordinary least squares projection for screening variables
High dimensional ordinary least squares projection for screening variables
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DOI：
10.1111/rssb.12127
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发表时间：
2016-06-01
影响因子：
5.8
通讯作者：
Leng, Chenlei
中科院分区：
文献类型：
--
作者：
Wang, Xiangyu;Leng, Chenlei
在统计应用中，当预测变量p的数量远远超过观测变量n的数量时，变量选择是一个具有挑战性的问题。在这个三维设置中，引入了确定的独立筛选程序，通过以压倒性的概率保留真实模型来显着降低维度，然后进行精细的第二阶段分析。然而，上述确定筛选属性强烈依赖于模型中的重要变量与响应具有大的边际相关性的假设，这在现实中很少成立。为了克服这一点，我们提出了一种新的和简单的筛选技术称为高维普通最小二乘投影，我们称之为“HOLP”。我们证明了HOLP具有确定的筛选性质，在没有强相关性假设的情况下，给出了一致的变量选择，并且具有较低的计算复杂度。本文还讨论了脊型HOLP方法。仿真结果表明，HOLP方法与其他基于边缘相关的方法相比具有很强的竞争力。一个哺乳动物眼病数据集的应用程序说明了HOLP的吸引力。
Variable selection is a challenging issue in statistical applications when the number of predictors p far exceeds the number of observations n. In this ultrahigh dimensional setting, the sure independence screening procedure was introduced to reduce the dimensionality significantly by preserving the true model with overwhelming probability, before a refined second-stage analysis. However, the aforementioned sure screening property strongly relies on the assumption that the important variables in the model have large marginal correlations with the response, which rarely holds in reality. To overcome this, we propose a novel and simple screening technique called high dimensional ordinary least squares projection which we refer to as 'HOLP'. We show that HOLP has the sure screening property and gives consistent variable selection without the strong correlation assumption, and it has a low computational complexity. A ridge-type HOLP procedure is also discussed. Simulation study shows that HOLP performs competitively compared with many other marginal correlation-based methods. An application to a mammalian eye disease data set illustrates the attractiveness of HOLP.