Testing generalized linear models with high-dimensional nuisance parameter.
Testing generalized linear models with high-dimensional nuisance parameter.
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DOI：
10.1093/biomet/asac021
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发表时间：
2022-04
期刊：
影响因子：
2.7
通讯作者：
Jinsong Chen;Quefeng Li;H. Y. Chen
中科院分区：
文献类型：
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作者：
Jinsong Chen;Quefeng Li;H. Y. Chen
普遍的线性模型通常具有高维的滋扰参数，如测试基因 - 环境相互作用或基因 - 基因相互作用等应用中所见。在这些情况下，必须测试模型系数的高维子矢量的重要性。尽管某些现有方法可以解决此问题，但它们通常依靠引导程序来近似测试统计量的渐近分布，因此计算上很昂贵。在这里，我们提出了具有封闭形式限制分布的计算有效测试，该测试允许被测试的参数稀疏或致密。我们表明，在某些规律性条件下，该方法的I型误差在渐近上是正确的，并且我们在高维替代方案下建立了其功率。广泛的模拟表明，当违反某些稀疏假设时，提出的测试及其稳健性的良好性能。我们还将提出的方法应用于中国饥荒样本数据，以在测试基因环境相互作用的重要性时显示其性能。
Generalized linear models often have a high-dimensional nuisance parameters, as seen in applications such as testing gene-environment interactions or gene-gene interactions. In these scenarios, it is essential to test the significance of a high-dimensional sub-vector of the model's coefficients. Although some existing methods can tackle this problem, they often rely on the bootstrap to approximate the asymptotic distribution of the test statistic, and thus are computationally expensive. Here, we propose a computationally efficient test with a closed-form limiting distribution, which allows the parameter being tested to be either sparse or dense. We show that under certain regularity conditions, the type I error of the proposed method is asymptotically correct, and we establish its power under high-dimensional alternatives. Extensive simulations demonstrate the good performance of the proposed test and its robustness when certain sparsity assumptions are violated. We also apply the proposed method to Chinese famine sample data in order to show its performance when testing the significance of gene-environment interactions.