A Regularization-Based Adaptive Test for High-Dimensional Generalized Linear Models
A Regularization-Based Adaptive Test for High-Dimensional Generalized Linear Models
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发表时间：
2020-07
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通讯作者：
Chong Wu;Gongjun Xu;Xiaotong Shen;W. Pan
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作者：
Chong Wu;Gongjun Xu;Xiaotong Shen;W. Pan
尽管在大数据时代具有紧迫的重要性，但在存在高维干扰参数的情况下测试广义线性模型（GLM）中的高维参数在很大程度上还没有得到充分研究，特别是在为一般（和未知）替代方案构建强大的测试方面。大多数现有测试仅针对某些替代方案有效，并且在高维干扰参数情况下可能会产生不正确的 I 类错误率。在本文中，我们提出了在带有非凸惩罚的惩罚回归框架中的自适应交互动力得分和（aiSPU）测试，称为截断套索惩罚（TLP），它可以保持正确的第一类错误率，同时在各种替代方案中产生高统计功效。为了分析计算其 p 值，我们推导出其渐近零分布。通过模拟，其优越的有限样本性能在几种代表性的现有方法中得到了证明。此外，我们将其和其他代表性测试应用于阿尔茨海默病神经影像计划 (ADNI) 数据集，检测阿尔茨海默病可能的基因-性别相互作用。我们还将 R 包“aispu”放在 GitHub 上实施建议的测试。
In spite of its urgent importance in the era of big data, testing high-dimensional parameters in generalized linear models (GLMs) in the presence of high-dimensional nuisance parameters has been largely under-studied, especially with regard to constructing powerful tests for general (and unknown) alternatives. Most existing tests are powerful only against certain alternatives and may yield incorrect Type I error rates under high-dimensional nuisance parameter situations. In this paper, we propose the adaptive interaction sum of powered score (aiSPU) test in the framework of penalized regression with a non-convex penalty, called truncated Lasso penalty (TLP), which can maintain correct Type I error rates while yielding high statistical power across a wide range of alternatives. To calculate its p-values analytically, we derive its asymptotic null distribution. Via simulations, its superior finite-sample performance is demonstrated over several representative existing methods. In addition, we apply it and other representative tests to an Alzheimer’s Disease Neuroimaging Initiative (ADNI) data set, detecting possible gene-gender interactions for Alzheimer’s disease. We also put R package “aispu” implementing the proposed test on GitHub.