Wu Chong, Xu Gongjun, Shen Xiaotong, Pan Wei
Department of Statistics, Florida State University, FL, USA.
Department of Statistics, University of Michigan, MI, USA.
J Mach Learn Res. 2020;21. Epub 2020 Jul 26.
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 -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 "" implementing the proposed test on GitHub.
尽管在大数据时代其具有紧迫性，但在存在高维干扰参数的情况下，对广义线性模型（GLMs）中的高维参数进行检验在很大程度上仍未得到充分研究，特别是在构建针对一般（且未知）备择假设的强大检验方面。大多数现有检验仅对某些备择假设有效，并且在高维干扰参数情况下可能会产生错误的第一类错误率。在本文中，我们在具有非凸惩罚（称为截断套索惩罚（TLP））的惩罚回归框架下提出了自适应幂得分交互和（aiSPU）检验，该检验可以保持正确的第一类错误率，同时在广泛的备择假设范围内具有高统计功效。为了通过解析计算其p值，我们推导了其渐近零分布。通过模拟，证明了它相对于几种有代表性的现有方法具有优越的有限样本性能。此外，我们将其与其他代表性检验应用于阿尔茨海默病神经影像倡议（ADNI）数据集，检测阿尔茨海默病可能的基因 - 性别相互作用。我们还在GitHub上发布了实现所提出检验的R包“”。
