Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models.
Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models.
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DOI：
10.1080/01621459.2019.1699421
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发表时间：
2021
影响因子：
3.7
通讯作者：
Li H
中科院分区：
文献类型：
--
作者：
Ma R;Cai TT;Li H
高维逻辑回归广泛用于分析具有二元结果的数据。在本文中，在单回归和双回归设置中考虑了回归系数的全局测试和大规模多重测试。使用广义低维投影来构建用于检验全局零假设的检验统计量以进行偏差校正，并导出其渐近零分布。建立了全局测试的下界，这表明所提出的测试在某些稀疏范围内是渐近最小最大最优的。为了同时测试各个系数，提出了多个测试程序，并证明可以渐近地控制错误发现率（FDR）和错误发现变量（FDV）。进行模拟研究是为了检验所提出的测试的数值性能及其相对于现有方法的优越性。还通过分析代谢组学研究的数据集来说明测试程序，该研究调查粪便代谢物与儿科克罗恩病之间的关联以及治疗对这种关联的影响。
High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this paper, global testing and large-scale multiple testing for the regression coefficients are considered in both single- and two-regression settings. A test statistic for testing the global null hypothesis is constructed using a generalized low-dimensional projection for bias correction and its asymptotic null distribution is derived. A lower bound for the global testing is established, which shows that the proposed test is asymptotically minimax optimal over some sparsity range. For testing the individual coefficients simultaneously, multiple testing procedures are proposed and shown to control the false discovery rate (FDR) and falsely discovered variables (FDV) asymptotically. Simulation studies are carried out to examine the numerical performance of the proposed tests and their superiority over existing methods. The testing procedures are also illustrated by analyzing a data set of a metabolomics study that investigates the association between fecal metabolites and pediatric Crohn’s disease and the effects of treatment on such associations.
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