Sufficient variable screening with high-dimensional controls

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY Electronic Journal of Statistics Pub Date : 2023-01-01 DOI:10.1214/23-ejs2150
Chenlu Ke
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Abstract

Variable screening for ultrahigh-dimensional data has attracted extensive attention in the past decade. In many applications, researchers learn from previous studies about certain important predictors or control variables related to the response of interest. Such knowledge should be taken into account in the screening procedure. The development of variable screening conditional on prior information, however, has been less fruitful, compared to the vast literature for generic unconditional screening. In this paper, we propose a model-free variable screening paradigm that allows for high-dimensional controls and applies to either continuous or categorical responses. The contribution of each individual predictor is quantified marginally and conditionally in the presence of the control variables as well as the other candidates by reproducing-kernel-based R2 and partial R2 statistics. As a result, the proposed method enjoys the sure screening property and the rank consistency property in the notion of sufficiency, with which its superiority over existing methods is well-established. The advantages of the proposed method are demonstrated by simulation studies encompassing a variety of regression and classification models, and an application to high-throughput gene expression data.
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充分的变量筛选与高维控制
超高维数据的可变筛选在过去的十年中引起了广泛的关注。在许多应用中,研究人员从先前的研究中了解到与兴趣反应相关的某些重要预测因子或控制变量。在筛选程序中应考虑到这些知识。然而,与大量的通用无条件筛选文献相比,基于先验信息的可变筛选的发展成果较少。在本文中,我们提出了一个无模型的变量筛选范式,允许高维控制,并适用于连续或分类响应。通过再现基于核的R2和部分R2统计,在控制变量以及其他候选变量存在的情况下,对每个个体预测因子的贡献进行边际和有条件的量化。结果表明,该方法在充分性概念下具有确定的筛选性和秩一致性,证明了其优于现有方法的优越性。包含各种回归和分类模型的模拟研究以及对高通量基因表达数据的应用证明了所提出方法的优势。
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来源期刊
Electronic Journal of Statistics
Electronic Journal of Statistics STATISTICS & PROBABILITY-
CiteScore
1.80
自引率
9.10%
发文量
100
审稿时长
3 months
期刊介绍: The Electronic Journal of Statistics (EJS) publishes research articles and short notes on theoretical, computational and applied statistics. The journal is open access. Articles are refereed and are held to the same standard as articles in other IMS journals. Articles become publicly available shortly after they are accepted.
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